Finite Group Databasebeta

← C2×#26021560 #36582354

Subgroups — C2×#26021560 #36582354

Order 22784.

1918 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667941C211yesmaximal, characteristic, complemented
2C22×#15667933C212yesmaximal, complemented
3C2×#19151501C212yesmaximal, complemented
4#26021560C218yesmaximal, direct product factor
5C2×#19151361C211yesmaximal, characteristic, complemented
6C23×D8×C89C211yesmaximal, characteristic
7C23×#10623494C2211yescharacteristic
8C22×C4⋊Dic89C2212yes—
9C22×C22⋊Dic89—22no—
10C22×C22⋊Dic89—22no—
11C22×C4×Dic89C2211yescharacteristic
12C2×#15667941—24no—
13C2×#15667941C2214yescomplemented
14C2×#15667933—28no—
15C2×#15667933C2218yescomplemented
16#19151501—24no—
17#19151501C2218yescomplemented
18#19151361C2214yescomplemented
19C23×D4×C89C2212yes—
20C22×D8×C89—28no—
21C22×D8×C89—24no—
22C22×D8×C89C2214yes—
23C23×C8×C89C2211yescharacteristic
24C23×Dic89—22no—
25C23×Dic89D411yescharacteristic
26C23×Dic89D411yescharacteristic
27C22×#10623494—22no—
28C22×#10623494—24no—
29C22×#10623494C2312yes—
30C2×C4⋊Dic89—24no—
31C2×C4⋊Dic89—22no—
32C2×C4⋊Dic89—24no—
33C2×C4⋊Dic89C2314yes—
34C2×C22⋊Dic89—28no—
35C2×C22⋊Dic89—28no—
36C2×C22⋊Dic89—48no—
37C2×C22⋊Dic89—48no—
38C2×C4×Dic89—22no—
39C2×C4×Dic89—22no—
40C2×C4×Dic89D412yes—
41C2×C4×Dic89C2312yes—
42#15667941—28no—
43#15667933—216no—
44C25×C89—22no—
45C22×D4×C89—24no—
46C22×D4×C89—24no—
47C22×D4×C89—22no—
48C22×D4×C89—24no—
49C22×D4×C89—24no—
50C22×D4×C89—24no—
51C22×D4×C89D418yes—
52C22×D4×C89C2314yes—
53C23×C4×C89C2311yescharacteristic
54C2×D8×C89—232no—
55C2×D8×C89—216no—
56C2×D8×C89—28no—
57C22×C8×C89—24no—
58C22×C8×C89D414yes—
59C22×C8×C89C2312yes—
60C22×Dic89—22no—
61C22×Dic89—22no—
62C22×Dic89—22no—
63C22×Dic89—24no—
64C22×Dic89—24no—
65C22×Dic89—44no—
66C22×Dic89—44no—
67C22×Dic89—44no—
68C22×Dic89D814yescomplemented
69C22×Dic89C2×D412yes—
70C22×Dic89C2×D412yes—
71C2×#10623494—24no—
72C2×#10623494—22no—
73C2×#10623494—44no—
74C4⋊Dic89—24no—
75C4⋊Dic89—24no—
76C4⋊Dic89—44no—
77C22⋊Dic89—416no—
78C22⋊Dic89—416no—
79C4×Dic89—24no—
80C4×Dic89—22no—
81C4×Dic89—22no—
82C24×C89—28no—
83C24×C89—24no—
84C24×C89—44no—
85C24×C89—44no—
86C24×C89—44no—
87C24×C89—44no—
88C24×C89—44no—
89C24×C89—44no—
90C24×C89C2×D411yescharacteristic
91C2×D4×C89—216no—
92C2×D4×C89—28no—
93C2×D4×C89—216no—
94C2×D4×C89—24no—
95C2×D4×C89—24no—
96C2×D4×C89—24no—
97C2×D4×C89—24no—
98C2×D4×C89—24no—
99C2×D4×C89—44no—
100C2×D4×C89—44no—
101C2×D4×C89—48no—
102C2×D4×C89—48no—
103C2×D4×C89C2×D418yes—
104C22×C4×C89C2×D414yes—
105C22×C4×C89C2×D412yes—
106C22×C4×C89C2×D411yescharacteristic
107C22×C4×C89#4112yes—
108C22×C4×C89#4114yes—
109C22×C4×C89C2411yescharacteristic
110D8×C89—232no—
111C2×C8×C89—28no—
112C2×C8×C89—24no—
113C2×C8×C89C2×D414yes—
114C23×C89—28no—
115C23×C89—44no—
116C23×C89—44no—
117C23×C89—44no—
118C23×C89—44no—
119C23×C89—44no—
120C23×C89—44no—
121C23×C89—416no—
122C23×C89—416no—
123C23×C89—416no—
124C23×C89—88no—
125C23×C89—88no—
126C23×C89—88no—
127C23×C89—88no—
128C23×C89#12112yes—
129C23×C89#12114yes—
130C23×C89C2×D812yes—
131C23×C89#13512yes—
132C23×C89AGL(1,ℤ/8)14yes—
133C23×C89C22×D411yescharacteristic
134D4×C89—28no—
135D4×C89—28no—
136D4×C89—44no—
137D4×C89—44no—
138D4×C89—416no—
139C2×C4×C89#12014yes—
140C2×C4×C89#12112yes—
141C2×C4×C89#12114yes—
142C2×C4×C89#12318yes—
143C2×C4×C89#12414yes—
144C2×C4×C89C22×D412yes—
145C2×C4×C89C22×D411yescharacteristic
146C2×C4×C89C2×#4111yescharacteristic
147C2×C4×C89C2×#4112yes—
148C2×Dic89—22no—
149C2×Dic89—22no—
150C2×Dic89—28no—
151C2×Dic89—22no—
152C2×Dic89—24no—
153C2×Dic89—44no—
154C2×Dic89—44no—
155C2×Dic89—44no—
156C2×Dic89—44no—
157C2×Dic89—88no—
158C2×Dic89C2×D814yescomplemented
159C8×C89—24no—
160#10623494—42no—
161C22×C89—48no—
162C22×C89—48no—
163C22×C89—48no—
164C22×C89—832no—
165C22×C89—84no—
166C22×C89—84no—
167C22×C89—84no—
168C22×C89—84no—
169C22×C89#39414yes—
170C22×C89#45918yes—
171C22×C89#46318yes—
172C22×C89#46614yes—
173C22×C89#46914yes—
174C22×C89C2×#12112yes—
175C22×C89C2×#12111yescharacteristic
176C22×C89C22×D811yescharacteristic
177C22×C89C2×#13511yescharacteristic
178C22×C89C2×AGL(1,ℤ/8)12yes—
179C4×C89#39414yes—
180C4×C89C2×#12011yescharacteristic
181C4×C89C2×#12312yes—
182C4×C89C2×#12411yescharacteristic
183Dic89—24no—
184Dic89—42no—
185Dic89—84no—
186C2×#2054—891nomaximal, Sylow
187C2×C89—88no—
188C2×C89#205418yescomplemented
189C2×C89C2×#39411yescharacteristic
190C2×C89C2×#45912yes—
191C2×C89C2×#46312yes—
192C2×C89C2×#46611yescharacteristic
193C2×C89C2×#46911yescharacteristic
194C23×D8D8911yescharacteristic
195C22×C4⋊C8—891no—
196C22×#102—892no—
197C2×#390—892no—
198#2054—898no—
199C2×#340—891no—
200C89C2×#205411yescharacteristic, complemented, Sylow
201C23×D4C2×D8912yes—
202C22×D8—28no—
203C22×D8—24no—
204C22×D8C2×D8914yes—
205C23×C8—891no—
206C23×C8C2×D8911yescharacteristic
207C22×C4⋊C4—892no—
208C22×C22⋊C4—1782no—
209C22×C22⋊C4—1782no—
210C22×C42—891no—
211C2×C4⋊C8—894no—
212C2×C4⋊C8—1784no—
213C2×#102—898no—
214C2×#102—1788no—
215#390—898no—
216#390—1784no—
217#340—894no—
218C25—22no—
219C22×D4—22no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4C22⋊D8918yes—
226C22×D4C22×D8914yes—
227C23×C4—891no—
228C23×C4—891no—
229C23×C4—1782no—
230C23×C4C22×D8911yescharacteristic
231C2×D8—232no—
232C2×D8—216no—
233C2×D8—28no—
234C22×C8—24no—
235C22×C8—892no—
236C22×C8—1784no—
237C22×C8—1782no—
238C22×C8C22⋊D8914yes—
239C22×C8C22×D8912yes—
240C2×C4⋊C4—894no—
241C2×C4⋊C4—1782no—
242C2×C4⋊C4—1784no—
243C2×C4⋊C4—1784no—
244C2×C22⋊C4—3568no—
245C2×C22⋊C4—3568no—
246C2×C22⋊C4—1788no—
247C2×C22⋊C4—1788no—
248C2×C42—892no—
249C2×C42—892no—
250C2×C42—1782no—
251C2×C42—1782no—
252C4⋊C8—1788no—
253#102—17816no—
254C24—28no—
255C24—24no—
256C24—44no—
257C24—44no—
258C24—44no—
259C24—44no—
260C24—44no—
261C24—44no—
262C24D4×D8911yescharacteristic
263C2×D4—216no—
264C2×D4—28no—
265C2×D4—216no—
266C2×D4—24no—
267C2×D4—24no—
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—48no—
274C2×D4—48no—
275C2×D4C2×C22⋊D8918yes—
276C22×C4—894no—
277C22×C4—892no—
278C22×C4—892no—
279C22×C4—3564no—
280C22×C4—3564no—
281C22×C4—3564no—
282C22×C4—1784no—
283C22×C4—1782no—
284C22×C4—1784no—
285C22×C4—1782no—
286C22×C4—1782no—
287C22×C4D4×D8911yescharacteristic
288C22×C4C2×C22⋊D8912yes—
289C22×C4C2×C22⋊D8914yes—
290C22×C4#1308357312yes—
291C22×C4#1308357314yes—
292C22×C4C23×D8911yescharacteristic
293D8—232no—
294C2×C8—28no—
295C2×C8—24no—
296C2×C8—3564no—
297C2×C8—1784no—
298C2×C8—1782no—
299C2×C8C2×C22⋊D8914yes—
300C4⋊C4—3564no—
301C4⋊C4—1784no—
302C4⋊C4—1784no—
303C22⋊C4—35616no—
304C22⋊C4—35616no—
305C42—1784no—
306C42—1782no—
307C42—1782no—
308C23—28no—
309C23—416no—
310C23—416no—
311C23—416no—
312C23—44no—
313C23—44no—
314C23—44no—
315C23—44no—
316C23—44no—
317C23—44no—
318C23—88no—
319C23—88no—
320C23—88no—
321C23—88no—
322C23#1566798312yes—
323C23#1566798414yes—
324C23D8×D8912yes—
325C23#1566803112yes—
326C23#1566803614yes—
327C23C2×D4×D8911yescharacteristic
328D4—28no—
329D4—28no—
330D4—416no—
331D4—44no—
332D4—44no—
333C2×C4—894no—
334C2×C4—3564no—
335C2×C4—3564no—
336C2×C4—3564no—
337C2×C4—3564no—
338C2×C4—1782no—
339C2×C4—1784no—
340C2×C4—1788no—
341C2×C4—1782no—
342C2×C4—1782no—
343C2×C4—7128no—
344C2×C4#1566798114yes—
345C2×C4#1566798312yes—
346C2×C4#1566798414yes—
347C2×C4#1566799318yes—
348C2×C4#1566799914yes—
349C2×C4C22×C22⋊D8912yes—
350C2×C4C22×C22⋊D8911yescharacteristic
351C2×C4C2×#1308357311yescharacteristic
352C2×C4C2×#1308357312yes—
353C8—24no—
354C8—3562no—
355C22—48no—
356C22—48no—
357C22—48no—
358C22—84no—
359C22—84no—
360C22—84no—
361C22—832no—
362C22—84no—
363C22#1915151214yes—
364C22#1915179118yes—
365C22#1915181118yes—
366C22#1915183114yes—
367C22#1915184814yes—
368C22C2×#1566798311yescharacteristic
369C22C2×#1566798412yes—
370C22C2×D8×D8911yescharacteristic
371C22C2×#1566803111yescharacteristic
372C22C2×#1566803612yes—
373C4—3562no—
374C4—1784no—
375C4—7124no—
376C4#1915151214yes—
377C4C2×#1566798111yescharacteristic
378C4C2×#1566799312yes—
379C4C2×#1566799911yescharacteristic
380C2—88no—
381C2#2602156018yesdirect product factor
382C2C2×#1915151211yescharacteristic
383C2C2×#1915179112yes—
384C2C2×#1915181112yes—
385C2C2×#1915183111yescharacteristic
386C2C2×#1915184811yescharacteristic
subgroupG/H
centerC24D4×D89
commutator, cosocleC22×C4×C89C24
FrattiniC22×C4C23×D89
Fitting, prime radicalC23×D8×C89C2
socleC24×C89C2×D4
hypercenterC23×D8D89
hypocenterC89C2×#2054
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

Complements

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

NH ≅ G/Ntype
1. C22×#15667941C2semidirect
2. C22×#15667933C2semidirect
3. C2×#19151501C2semidirect
4. #26021560C2direct (N × H)
5. C2×#19151361C2semidirect
13. C2×#15667941C22semidirect
15. C2×#15667933C22semidirect
17. #19151501C22semidirect
18. #19151361C22semidirect
68. C22×Dic89D8semidirect
158. C2×Dic89C2×D8semidirect
188. C2×C89#2054semidirect
200. C89C2×#2054semidirect
381. C2#26021560direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679412
C22×#156679332
C2×#191515012
#260215602
C2×#191513612
C23×D8×C892
C2×#205489