Finite Group Databasebeta

← C2×#26021815 #36584336

Subgroups — C2×#26021815 #36584336

Order 22784.

998 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
1C2×#19151468C211yesmaximal, characteristic
2#26021815C218yesmaximal, direct product factor
3C2×#19151360C212yesmaximal
4C2×#19151360C212yesmaximal
5C2×#19151353C211yesmaximal, characteristic
6C2×#389×C89C211yesmaximal, characteristic
7C23×#10623494C2212yes—
8C22×C4⋊Dic89—21no—
9C22×C4⋊Dic89—21no—
10C22×C4⋊Dic89C2212yes—
11#19151468—22no—
12#19151468C2214yes—
13#19151360C2218yes—
14#19151360C2218yes—
15#19151353C2214yes—
16C22×C4⋊C4×C89—21no—
17C22×C4⋊C4×C89C2211yescharacteristic
18C22×C4⋊C4×C89C2211yescharacteristic
19C22×C42×C89C2211yescharacteristic
20#389×C89—22no—
21#389×C89C2214yes—
22C2×#95×C89—21no—
23C23×Dic89—22no—
24C22×#10623494—24no—
25C22×#10623494—24no—
26C22×#10623494—24no—
27C22×#10623494C2314yes—
28C2×C4⋊Dic89—22no—
29C2×C4⋊Dic89—24no—
30C2×C4⋊Dic89—24no—
31C2×C4⋊Dic89—28no—
32C2×C4⋊Dic89—44no—
33C2×C4⋊Dic89—44no—
34C2×C4⋊Dic89C2314yes—
35C23×C4×C89—21no—
36C23×C4×C89—21no—
37C23×C4×C89D411yescharacteristic
38C23×C4×C89D411yescharacteristic
39C23×C4×C89C2311yescharacteristic
40C2×C4⋊C4×C89—21no—
41C2×C4⋊C4×C89—22no—
42C2×C4⋊C4×C89—24no—
43C2×C4⋊C4×C89—21no—
44C2×C4⋊C4×C89—24no—
45C2×C4⋊C4×C89—44no—
46C2×C4⋊C4×C89Q814yes—
47C2×C4⋊C4×C89C2312yes—
48C2×C4⋊C4×C89C2312yes—
49C2×C42×C89—24no—
50C2×C42×C89D412yes—
51C2×C42×C89C2312yes—
52#95×C89—24no—
53C22×Dic89—24no—
54C22×Dic89—44no—
55C22×Dic89—44no—
56C22×Dic89—44no—
57C2×#10623494—24no—
58C2×#10623494—24no—
59C2×#10623494—24no—
60C2×#10623494—48no—
61C4⋊Dic89—28no—
62C4⋊Dic89—48no—
63C4⋊Dic89—48no—
64C4⋊Dic89—44no—
65C24×C89C2×D411yescharacteristic
66C22×C4×C89—22no—
67C22×C4×C89—22no—
68C22×C4×C89—22no—
69C22×C4×C89—22no—
70C22×C4×C89—24no—
71C22×C4×C89—22no—
72C22×C4×C89—22no—
73C22×C4×C89—42no—
74C22×C4×C89—42no—
75C22×C4×C89—42no—
76C22×C4×C89—42no—
77C22×C4×C89—42no—
78C22×C4×C89SD1614yes—
79C22×C4×C89Q1614yes—
80C22×C4×C89C2×D412yes—
81C22×C4×C89C2×D412yes—
82C22×C4×C89C2×D411yescharacteristic
83C22×C4×C89C2×Q812yes—
84C22×C4×C89#4112yes—
85C22×C4×C89#4114yes—
86C22×C4×C89#4114yes—
87C22×C4×C89C2411yescharacteristic
88C4⋊C4×C89—24no—
89C4⋊C4×C89—22no—
90C4⋊C4×C89—24no—
91C4⋊C4×C89—42no—
92C4⋊C4×C89—48no—
93C4⋊C4×C89C2×Q814yes—
94C42×C89—24no—
95C42×C89—24no—
96C23×C89C22⋊Q812yes—
97C23×C89#12312yes—
98C23×C89#12412yes—
99C23×C89C2×SD1612yes—
100C23×C89C2×Q1612yes—
101C23×C89AGL(1,ℤ/8)12yes—
102C23×C89AGL(1,ℤ/8)12yes—
103C23×C89C22×D411yescharacteristic
104C2×C4×C89—22no—
105C2×C4×C89—22no—
106C2×C4×C89—22no—
107C2×C4×C89—22no—
108C2×C4×C89—28no—
109C2×C4×C89—28no—
110C2×C4×C89—24no—
111C2×C4×C89—42no—
112C2×C4×C89—42no—
113C2×C4×C89—48no—
114C2×C4×C89—42no—
115C2×C4×C89—42no—
116C2×C4×C89—42no—
117C2×C4×C89—84no—
118C2×C4×C89C22⋊Q812yes—
119C2×C4×C89#12312yes—
120C2×C4×C89#12412yes—
121C2×C4×C89#12518yes—
122C2×C4×C89#12618yes—
123C2×C4×C89C2×SD1614yes—
124C2×C4×C89C2×Q1614yes—
125C2×C4×C89C22×Q811yescharacteristic
126C2×C4×C89C2×#4112yes—
127C2×C4×C89C2×#4111yescharacteristic
128C2×C4×C89C2×#4112yes—
129C2×Dic89—44no—
130C2×Dic89—44no—
131C2×Dic89—44no—
132C2×Dic89—88no—
133#10623494—44no—
134C22×C89#40014yes—
135C22×C89#47614yes—
136C22×C89#47714yes—
137C22×C89#48114yes—
138C22×C89#48414yes—
139C22×C89#48714yes—
140C22×C89#49014yes—
141C22×C89C2×C22⋊Q811yescharacteristic
142C22×C89C2×#12311yescharacteristic
143C22×C89C2×#12411yescharacteristic
144C22×C89C22×SD1611yescharacteristic
145C22×C89C22×Q1611yescharacteristic
146C22×C89C2×AGL(1,ℤ/8)11yescharacteristic
147C22×C89C2×AGL(1,ℤ/8)11yescharacteristic
148C4×C89—24no—
149C4×C89—24no—
150C4×C89—44no—
151C4×C89—82no—
152C4×C89#40014yes—
153C4×C89C2×#12512yes—
154C4×C89C2×#12612yes—
155Dic89—84no—
156C2×#2100—891nomaximal, Sylow
157C2×C89#210018yescomplemented
158C2×C89C2×#40011yescharacteristic
159C2×C89C2×#47611yescharacteristic
160C2×C89C2×#47711yescharacteristic
161C2×C89C2×#48111yescharacteristic
162C2×C89C2×#48411yescharacteristic
163C2×C89C2×#48711yescharacteristic
164C2×C89C2×#49011yescharacteristic
165C2×#389D8911yescharacteristic
166C2×#384—891no—
167#2100—898no—
168C2×#340—892no—
169C2×#340—892no—
170C2×#336—891no—
171C89C2×#210011yescharacteristic, complemented, Sylow
172C23×C8—892no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—892no—
175C22×C4⋊C4—1781no—
176C22×C4⋊C4—1781no—
177C22×C4⋊C4C2×D8911yescharacteristic
178C22×C4⋊C4C2×D8911yescharacteristic
179C22×C42C2×D8911yescharacteristic
180#389—22no—
181#389C2×D8914yes—
182#384—894no—
183#384—1782no—
184C2×#95—21no—
185#340—898no—
186#340—898no—
187#336—894no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—1782no—
191C23×C4C22⋊D8911yescharacteristic
192C23×C4C22⋊D8911yescharacteristic
193C23×C4C22×D8911yescharacteristic
194C22×C8—894no—
195C22×C8—1784no—
196C22×C8—1784no—
197C22×C8—1784no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—44no—
204C2×C4⋊C4—894no—
205C2×C4⋊C4—3564no—
206C2×C4⋊C4—3564no—
207C2×C4⋊C4—1782no—
208C2×C4⋊C4—1784no—
209C2×C4⋊C4—1784no—
210C2×C4⋊C4—1788no—
211C2×C4⋊C4Dic17814yes—
212C2×C4⋊C4C22×D8912yes—
213C2×C4⋊C4C22×D8912yes—
214C2×C42—24no—
215C2×C42C22⋊D8912yes—
216C2×C42C22×D8912yes—
217#95—24no—
218C24C2×C22⋊D8911yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—24no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—3564no—
232C22×C4—3564no—
233C22×C4—3564no—
234C22×C4—1784no—
235C22×C4#1308356214yes—
236C22×C4#1308356414yes—
237C22×C4C2×C22⋊D8912yes—
238C22×C4C2×C22⋊D8912yes—
239C22×C4C2×C22⋊D8911yescharacteristic
240C22×C4C2×Dic17812yes—
241C22×C4#1308357314yes—
242C22×C4#1308357412yes—
243C22×C4#1308357514yes—
244C22×C4C23×D8911yescharacteristic
245C2×C8—3568no—
246C2×C8—1784no—
247C2×C8—1784no—
248C2×C8—1784no—
249C4⋊C4—24no—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—42no—
253C4⋊C4—48no—
254C4⋊C4—3568no—
255C4⋊C4—3568no—
256C4⋊C4—3564no—
257C4⋊C4—1788no—
258C4⋊C4C2×Dic17814yes—
259C42—24no—
260C42—24no—
261C23#1566799112yes—
262C23#1566799312yes—
263C23#1566800112yes—
264C23C2×#1308356212yes—
265C23C2×#1308356412yes—
266C23#1566803712yes—
267C23#1566803712yes—
268C23C22×C22⋊D8911yescharacteristic
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—28no—
272C2×C4—28no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—42no—
277C2×C4—48no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—84no—
283C2×C4—3564no—
284C2×C4—3564no—
285C2×C4—3564no—
286C2×C4—7128no—
287C2×C4#1566799112yes—
288C2×C4#1566799312yes—
289C2×C4#1566800112yes—
290C2×C4#1566800318yes—
291C2×C4#1566800718yes—
292C2×C4C2×#1308356214yes—
293C2×C4C2×#1308356414yes—
294C2×C4C22×Dic17811yescharacteristic
295C2×C4C2×#1308357312yes—
296C2×C4C2×#1308357411yescharacteristic
297C2×C4C2×#1308357512yes—
298C8—3564no—
299C22#1915153714yes—
300C22#1915188814yes—
301C22#1915189314yes—
302C22#1915191414yes—
303C22#1915193114yes—
304C22#1915195014yes—
305C22#1915196414yes—
306C22C2×#1566799111yescharacteristic
307C22C2×#1566799311yescharacteristic
308C22C2×#1566800111yescharacteristic
309C22C22×#1308356211yescharacteristic
310C22C22×#1308356411yescharacteristic
311C22C2×#1566803711yescharacteristic
312C22C2×#1566803711yescharacteristic
313C4—24no—
314C4—24no—
315C4—44no—
316C4—82no—
317C4—7124no—
318C4#1915153714yes—
319C4C2×#1566800312yes—
320C4C2×#1566800712yes—
321C2#2602181518yesdirect product factor
322C2C2×#1915153711yescharacteristic
323C2C2×#1915188811yescharacteristic
324C2C2×#1915189311yescharacteristic
325C2C2×#1915191411yescharacteristic
326C2C2×#1915193111yescharacteristic
327C2C2×#1915195011yescharacteristic
328C2C2×#1915196411yescharacteristic
subgroupG/H
centerC24C2×C22⋊D89
commutator, cosocleC22×C4×C89C24
FrattiniC22×C4C23×D89
FittingC2×#389×C89C2
socle, prime radicalC24×C89C2×D4
hypercenterC2×#389D89
hypocenterC89C2×#2100
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. #26021815C2direct (N × H)
157. C2×C89#2100semidirect
171. C89C2×#2100semidirect
321. C2#26021815direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191514682
#260218152
C2×#191513602
C2×#191513532
C2×#389×C892
C2×#210089