Finite Group Databasebeta

← C22×#19151360 #36551823

Subgroups — C22×#19151360 #36551823

Order 22784.

3006 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×#10623494C211yesmaximal, characteristic
2C23×C4⋊Dic89C211yesmaximal, characteristic
3C2×#19151360C2112yesmaximal, direct product factor
4C23×C4⋊C4×C89C211yesmaximal, characteristic
5C24×Dic89—21no—
6C23×#10623494—24no—
7C23×#10623494—24no—
8C23×#10623494C418yescomplemented
9C23×#10623494C2216yes—
10C22×C4⋊Dic89—24no—
11C22×C4⋊Dic89—23no—
12C22×C4⋊Dic89C418yescomplemented
13C22×C4⋊Dic89C2216yes—
14#19151360C22116yesdirect product factor
15C24×C4×C89—21no—
16C24×C4×C89C2211yescharacteristic
17C22×C4⋊C4×C89—23no—
18C22×C4⋊C4×C89—24no—
19C22×C4⋊C4×C89C418yescomplemented
20C22×C4⋊C4×C89C2216yes—
21C23×Dic89—28no—
22C23×Dic89—26no—
23C23×Dic89—44no—
24C23×Dic89—44no—
25C22×#10623494—232no—
26C22×#10623494—212no—
27C22×#10623494—212no—
28C22×#10623494C2×C4124yescomplemented
29C22×#10623494C2314yes—
30C2×C4⋊Dic89—224no—
31C2×C4⋊Dic89—26no—
32C2×C4⋊Dic89—212no—
33C2×C4⋊Dic89C2×C4124yescomplemented
34C2×C4⋊Dic89C2314yes—
35C25×C89D411yescharacteristic
36C23×C4×C89—28no—
37C23×C4×C89—26no—
38C23×C4×C89—44no—
39C23×C4×C89—44no—
40C23×C4×C89C2×C414yes—
41C23×C4×C89C2×C414yes—
42C23×C4×C89C2×C414yes—
43C23×C4×C89D414yes—
44C23×C4×C89D413yes—
45C23×C4×C89D414yes—
46C23×C4×C89Q814yes—
47C23×C4×C89C2313yes—
48C2×C4⋊C4×C89—224no—
49C2×C4⋊C4×C89—26no—
50C2×C4⋊C4×C89—212no—
51C2×C4⋊C4×C89C2×C4124yescomplemented
52C2×C4⋊C4×C89C2314yes—
53C22×Dic89—224no—
54C22×Dic89—24no—
55C22×Dic89—432no—
56C22×Dic89—412no—
57C22×Dic89—412no—
58C2×#10623494—248no—
59C2×#10623494—24no—
60C2×#10623494—24no—
61C2×#10623494C22×C418yescomplemented
62C4⋊Dic89—224no—
63C4⋊Dic89—24no—
64C4⋊Dic89C22×C418yescomplemented
65C24×C89C22⋊C414yes—
66C24×C89C22⋊C414yes—
67C24×C89C4⋊C414yes—
68C24×C89D814yes—
69C24×C89SD1614yes—
70C24×C89SD1614yes—
71C24×C89Q1614yes—
72C24×C89C2×D413yes—
73C22×C4×C89—224no—
74C22×C4×C89—24no—
75C22×C4×C89—432no—
76C22×C4×C89—412no—
77C22×C4×C89—412no—
78C22×C4×C89C42116yes—
79C22×C4×C89C22⋊C4112yes—
80C22×C4×C89C22⋊C4112yes—
81C22×C4×C89C22⋊C4116yes—
82C22×C4×C89C4⋊C4112yes—
83C22×C4×C89C4⋊C4116yes—
84C22×C4×C89C4⋊C4116yes—
85C22×C4×C89C22×C416yes—
86C22×C4×C89C22×C416yes—
87C22×C4×C89C22×C416yes—
88C22×C4×C89C2×D413yes—
89C22×C4×C89C2×D416yes—
90C22×C4×C89C2×D416yes—
91C22×C4×C89C2×Q816yes—
92C22×C4×C89C2411yescharacteristic
93C4⋊C4×C89—224no—
94C4⋊C4×C89—24no—
95C4⋊C4×C89C22×C418yescomplemented
96C23×C89#95116yes—
97C23×C89#102116yes—
98C23×C89#102116yes—
99C23×C89#103116yes—
100C23×C89#103116yes—
101C23×C89#106116yes—
102C23×C89#107116yes—
103C23×C89C2×C22⋊C416yes—
104C23×C89C2×C22⋊C416yes—
105C23×C89C2×C4⋊C416yes—
106C23×C89C2×D816yes—
107C23×C89C2×SD1616yes—
108C23×C89C2×SD1616yes—
109C23×C89C2×Q1616yes—
110C23×C89C22×D411yescharacteristic
111C2×C4×C89—28no—
112C2×C4×C89—44no—
113C2×C4×C89—44no—
114C2×C4×C89—448no—
115C2×C4×C89#95148yes—
116C2×C4×C89C2×C42112yes—
117C2×C4×C89C2×C22⋊C4112yes—
118C2×C4×C89C2×C22⋊C416yes—
119C2×C4×C89C2×C22⋊C416yes—
120C2×C4×C89C2×C4⋊C4112yes—
121C2×C4×C89C2×C4⋊C416yes—
122C2×C4×C89C2×C4⋊C4112yes—
123C2×C4×C89C23×C411yescharacteristic
124C2×C4×C89C23×C411yescharacteristic
125C2×C4×C89C23×C411yescharacteristic
126C2×C4×C89C22×D411yescharacteristic
127C2×C4×C89C22×D411yescharacteristic
128C2×C4×C89C22×Q811yescharacteristic
129C2×Dic89—28no—
130C2×Dic89—44no—
131C2×Dic89—44no—
132C2×Dic89—448no—
133#10623494—28no—
134C22×C89#340164yescomplemented
135C22×C89C2×#95112yes—
136C22×C89C2×#102112yes—
137C22×C89C2×#102112yes—
138C22×C89C2×#103112yes—
139C22×C89C2×#103112yes—
140C22×C89C2×#106112yes—
141C22×C89C2×#107112yes—
142C22×C89C22×C22⋊C411yescharacteristic
143C22×C89C22×C22⋊C411yescharacteristic
144C22×C89C22×C4⋊C411yescharacteristic
145C22×C89C22×D811yescharacteristic
146C22×C89C22×SD1611yescharacteristic
147C22×C89C22×SD1611yescharacteristic
148C22×C89C22×Q1611yescharacteristic
149C4×C89—48no—
150C4×C89C2×#95112yes—
151C4×C89C22×C4211yescharacteristic
152C4×C89C22×C22⋊C411yescharacteristic
153C4×C89C22×C4⋊C411yescharacteristic
154C4×C89C22×C4⋊C411yescharacteristic
155Dic89—48no—
156C22×#340—891nomaximal, Sylow
157C2×C89C2×#340124yescomplemented
158C2×C89C22×#9511yescharacteristic
159C2×C89C22×#10211yescharacteristic
160C2×C89C22×#10211yescharacteristic
161C2×C89C22×#10311yescharacteristic
162C2×C89C22×#10311yescharacteristic
163C2×C89C22×#10611yescharacteristic
164C2×C89C22×#10711yescharacteristic
165C24×C8—891no—
166C23×C4⋊C4—891no—
167C23×C4⋊C4D8911yescharacteristic
168C2×#340—8912no—
169C89C22×#34011yescharacteristic, complemented, Sylow
170C24×C4—21no—
171C24×C4—1781no—
172C24×C4C2×D8911yescharacteristic
173C23×C8—898no—
174C23×C8—896no—
175C23×C8—1784no—
176C23×C8—1784no—
177C22×C4⋊C4—23no—
178C22×C4⋊C4—24no—
179C22×C4⋊C4—898no—
180C22×C4⋊C4—896no—
181C22×C4⋊C4—1784no—
182C22×C4⋊C4—1783no—
183C22×C4⋊C4Dic8918yescomplemented
184C22×C4⋊C4C2×D8916yes—
185#340—8916no—
186C25C22⋊D8911yescharacteristic
187C23×C4—28no—
188C23×C4—26no—
189C23×C4—44no—
190C23×C4—44no—
191C23×C4—3564no—
192C23×C4—3564no—
193C23×C4—1788no—
194C23×C4—1786no—
195C23×C4Dic17814yes—
196C23×C4C4×D8914yes—
197C23×C4C4×D8914yes—
198C23×C4D35614yes—
199C23×C4C2×Dic8914yes—
200C23×C4C22⋊D8913yes—
201C23×C4C22⋊D8914yes—
202C23×C4C22×D8913yes—
203C22×C8—8924no—
204C22×C8—894no—
205C22×C8—17832no—
206C22×C8—17812no—
207C22×C8—17812no—
208C2×C4⋊C4—224no—
209C2×C4⋊C4—212no—
210C2×C4⋊C4—26no—
211C2×C4⋊C4—8924no—
212C2×C4⋊C4—894no—
213C2×C4⋊C4—17824no—
214C2×C4⋊C4—1786no—
215C2×C4⋊C4—17812no—
216C2×C4⋊C4C2×Dic89124yescomplemented
217C2×C4⋊C4C22×D8914yes—
218C24#1308355114yes—
219C24C22⋊Dic8914yes—
220C24#1308355314yes—
221C24#1308355914yes—
222C24#1308356114yes—
223C24#1308356214yes—
224C24#1308356414yes—
225C24C2×C22⋊D8913yes—
226C22×C4—24no—
227C22×C4—224no—
228C22×C4—412no—
229C22×C4—412no—
230C22×C4—432no—
231C22×C4—35612no—
232C22×C4—35612no—
233C22×C4—35632no—
234C22×C4—1784no—
235C22×C4—17824no—
236C22×C4C4×Dic89116yes—
237C22×C4#13083551112yes—
238C22×C4#13083551116yes—
239C22×C4C22⋊Dic89112yes—
240C22×C4#13083553112yes—
241C22×C4#13083553116yes—
242C22×C4C4⋊Dic89116yes—
243C22×C4C2×C4×D8916yes—
244C22×C4C2×C4×D8916yes—
245C22×C4C22×Dic8916yes—
246C22×C4C2×C22⋊D8916yes—
247C22×C4C2×C22⋊D8913yes—
248C22×C4C2×D35616yes—
249C22×C4C2×Dic17816yes—
250C22×C4C23×D8911yescharacteristic
251C2×C8—898no—
252C2×C8—1784no—
253C2×C8—1784no—
254C2×C8—17848no—
255C4⋊C4—24no—
256C4⋊C4—224no—
257C4⋊C4—898no—
258C4⋊C4—1784no—
259C4⋊C4—17824no—
260C4⋊C4C22×Dic8918yescomplemented
261C23#15667919116yes—
262C23#15667932116yes—
263C23#15667933116yes—
264C23#15667935116yes—
265C23#15667936116yes—
266C23#15667943116yes—
267C23#15667945116yes—
268C23C2×#1308355116yes—
269C23C2×C22⋊Dic8916yes—
270C23C2×#1308355316yes—
271C23C2×#1308355916yes—
272C23C2×#1308356116yes—
273C23C2×#1308356216yes—
274C23C2×#1308356416yes—
275C23C22×C22⋊D8911yescharacteristic
276C2×C4—28no—
277C2×C4—448no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—35648no—
281C2×C4—3564no—
282C2×C4—3564no—
283C2×C4—1788no—
284C2×C4#15667919148yes—
285C2×C4C2×C4×Dic89112yes—
286C2×C4C2×#1308355116yes—
287C2×C4C2×#13083551112yes—
288C2×C4C2×C22⋊Dic8916yes—
289C2×C4C2×#1308355316yes—
290C2×C4C2×#13083553112yes—
291C2×C4C2×C4⋊Dic89112yes—
292C2×C4C22×C4×D8911yescharacteristic
293C2×C4C22×C4×D8911yescharacteristic
294C2×C4C23×Dic8911yescharacteristic
295C2×C4C22×C22⋊D8911yescharacteristic
296C2×C4C22×D35611yescharacteristic
297C2×C4C22×Dic17811yescharacteristic
298C8—1788no—
299C22#19151360164yesdirect product factor
300C22C2×#15667919112yes—
301C22C2×#15667932112yes—
302C22C2×#15667933112yes—
303C22C2×#15667935112yes—
304C22C2×#15667936112yes—
305C22C2×#15667943112yes—
306C22C2×#15667945112yes—
307C22C22×#1308355111yescharacteristic
308C22C22×C22⋊Dic8911yescharacteristic
309C22C22×#1308355311yescharacteristic
310C22C22×#1308355911yescharacteristic
311C22C22×#1308356111yescharacteristic
312C22C22×#1308356211yescharacteristic
313C22C22×#1308356411yescharacteristic
314C4—48no—
315C4—3568no—
316C4C2×#15667919112yes—
317C4C22×C4×Dic8911yescharacteristic
318C4C22×#1308355111yescharacteristic
319C4C22×#1308355311yescharacteristic
320C4C22×C4⋊Dic8911yescharacteristic
321C2C2×#19151360124yesdirect product factor
322C2C22×#1566791911yescharacteristic
323C2C22×#1566793211yescharacteristic
324C2C22×#1566793311yescharacteristic
325C2C22×#1566793511yescharacteristic
326C2C22×#1566793611yescharacteristic
327C2C22×#1566794311yescharacteristic
328C2C22×#1566794511yescharacteristic
subgroupG/H
centerC25C22⋊D89
commutatorC4×C89C22×C42
FrattiniC22×C4C23×D89
FittingC23×C4⋊C4×C89C2
socle, prime radicalC25×C89D4
cosocleC22×C4×C89C24
hypercenterC23×C4⋊C4D89
hypocenterC89C22×#340
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#19151360C2direct (N × H)
8. C23×#10623494C4semidirect
12. C22×C4⋊Dic89C4semidirect
14. #19151360C22direct (N × H)
19. C22×C4⋊C4×C89C4semidirect
28. C22×#10623494C2×C4semidirect
33. C2×C4⋊Dic89C2×C4semidirect
51. C2×C4⋊C4×C89C2×C4semidirect
61. C2×#10623494C22×C4semidirect
64. C4⋊Dic89C22×C4semidirect
95. C4⋊C4×C89C22×C4semidirect
134. C22×C89#340semidirect
157. C2×C89C2×#340semidirect
169. C89C22×#340semidirect
183. C22×C4⋊C4Dic89semidirect
216. C2×C4⋊C4C2×Dic89semidirect
260. C4⋊C4C22×Dic89semidirect
299. C22#19151360direct (N × H)
321. C2C2×#19151360direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#106234942
C23×C4⋊Dic892
C2×#191513602
C23×C4⋊C4×C892
C22×#34089