Finite Group Databasebeta

← C2×#26020360 #36554283

Subgroups — C2×#26020360 #36554283

Order 22784.

1554 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667927C212yesmaximal
2#26020360C218yesmaximal, direct product factor
3C2×#19151364C214yesmaximal, complemented
4C2×#518×C89C211yesmaximal, characteristic
5C22×C22⋊Dic89C2214yes—
6C2×#15667927—24no—
7C2×#15667927—24no—
8C2×#15667927C2218yes—
9#19151364C22116yescomplemented
10C23×D4×C89C2211yescharacteristic
11#518×C89—24no—
12#518×C89C414yescomplemented
13#518×C89C2214yes—
14C2×C4×D4×C89—24no—
15C2×#117×C89C412yescomplemented
16C22×C22⋊C4×C89C412yescomplemented
17C22×C22⋊C4×C89C2212yes—
18C23×Dic89—24no—
19C2×C22⋊Dic89—24no—
20C2×C22⋊Dic89—24no—
21C2×C22⋊Dic89—24no—
22C2×C22⋊Dic89—24no—
23C2×C22⋊Dic89—24no—
24C2×C22⋊Dic89C2318yes—
25#15667927—216no—
26C25×C89C2×C411yescharacteristic
27C25×C89C2311yescharacteristic
28C22×D4×C89—24no—
29C22×D4×C89—24no—
30C22×D4×C89C2×C412yes—
31C22×D4×C89D414yes—
32C22×D4×C89D414yes—
33C22×D4×C89C2312yes—
34C23×C4×C89—22no—
35C23×C4×C89—22no—
36C23×C4×C89C2×C411yescharacteristic
37C4×D4×C89—216no—
38C4×D4×C89—216no—
39#117×C89—24no—
40#117×C89C2×C418yescomplemented
41C2×C4⋊C4×C89—22no—
42C2×C22⋊C4×C89—22no—
43C2×C22⋊C4×C89—24no—
44C2×C22⋊C4×C89—22no—
45C2×C22⋊C4×C89—22no—
46C2×C22⋊C4×C89—22no—
47C2×C22⋊C4×C89C2×C414yes—
48C2×C22⋊C4×C89C2×C414yes—
49C2×C22⋊C4×C89C2×C418yescomplemented
50C2×C22⋊C4×C89C2314yes—
51C2×C42×C89—22no—
52C22×Dic89—28no—
53C22×Dic89—44no—
54C22×Dic89—44no—
55C22×Dic89—88no—
56C22⋊Dic89—28no—
57C22⋊Dic89—28no—
58C22⋊Dic89—44no—
59C22⋊Dic89—44no—
60C24×C89—22no—
61C24×C89—22no—
62C24×C89—82no—
63C24×C89—82no—
64C24×C89C22⋊C412yes—
65C24×C89C22⋊C412yes—
66C24×C89C22×C412yes—
67C24×C89C22×C411yescharacteristic
68C24×C89C22×C411yescharacteristic
69C24×C89C2×D412yes—
70C24×C89C2×D412yes—
71C24×C89#4114yes—
72C24×C89#4114yes—
73C24×C89C2411yescharacteristic
74C2×D4×C89—28no—
75C2×D4×C89—28no—
76C2×D4×C89—28no—
77C2×D4×C89—28no—
78C2×D4×C89—28no—
79C2×D4×C89—28no—
80C2×D4×C89C22⋊C418yes—
81C2×D4×C89C2×D418yes—
82C22×C4×C89—22no—
83C22×C4×C89—22no—
84C22×C4×C89—24no—
85C22×C4×C89—24no—
86C22×C4×C89—28no—
87C22×C4×C89—24no—
88C22×C4×C89—84no—
89C22×C4×C89—84no—
90C22×C4×C89C22⋊C412yes—
91C22×C4×C89C22⋊C412yes—
92C22×C4×C89C22×C412yes—
93C4⋊C4×C89—28no—
94C22⋊C4×C89—24no—
95C22⋊C4×C89—24no—
96C22⋊C4×C89—28no—
97C22⋊C4×C89—24no—
98C22⋊C4×C89C22×C418yes—
99C42×C89—28no—
100C23×C89—22no—
101C23×C89—22no—
102C23×C89—24no—
103C23×C89—24no—
104C23×C89—44no—
105C23×C89—42no—
106C23×C89—48no—
107C23×C89—44no—
108C23×C89—84no—
109C23×C89—81no—
110C23×C89—82no—
111C23×C89—84no—
112C23×C89—81no—
113C23×C89—82no—
114C23×C89—82no—
115C23×C89—84no—
116C23×C89C2×C22⋊C411yescharacteristic
117C23×C89C2×C22⋊C414yes—
118C23×C89C2×C22⋊C411yescharacteristic
119C23×C89C2×C22⋊C412yes—
120C23×C89#11712yes—
121C23×C89#11712yes—
122C23×C89#11714yes—
123C23×C89#12314yes—
124C23×C89#12314yes—
125C23×C89#12314yes—
126C23×C89#12314yes—
127C23×C89C23×C411yescharacteristic
128C23×C89C22×D412yes—
129C23×C89C2×#4114yes—
130D4×C89—216no—
131D4×C89—216no—
132C2×C4×C89—24no—
133C2×C4×C89—22no—
134C2×C4×C89—24no—
135C2×C4×C89—22no—
136C2×C4×C89—28no—
137C2×C4×C89—48no—
138C2×C4×C89—84no—
139C2×C4×C89—84no—
140C2×C4×C89—88no—
141C2×C4×C89C2×C22⋊C414yes—
142C2×Dic89—48no—
143C2×Dic89—88no—
144C2×Dic89—88no—
145C2×Dic89—88no—
146C22×C89—28no—
147C22×C89—22no—
148C22×C89—24no—
149C22×C89—24no—
150C22×C89—44no—
151C22×C89—44no—
152C22×C89—42no—
153C22×C89—42no—
154C22×C89—41no—
155C22×C89—42no—
156C22×C89—41no—
157C22×C89—44no—
158C22×C89—44no—
159C22×C89—44no—
160C22×C89—44no—
161C22×C89—44no—
162C22×C89—44no—
163C22×C89—84no—
164C22×C89—84no—
165C22×C89#38111yescharacteristic
166C22×C89#38112yes—
167C22×C89#38114yes—
168C22×C89#38111yescharacteristic
169C22×C89C22×C22⋊C411yescharacteristic
170C22×C89C2×#11712yes—
171C22×C89C2×#12314yes—
172C4×C89—24no—
173C4×C89—48no—
174Dic89—88no—
175C2×#1828—891nomaximal, Sylow
176C2×C89—24no—
177C2×C89—21no—
178C2×C89—21no—
179C2×C89—22no—
180C2×C89—22no—
181C2×C89—24no—
182C2×C89—44no—
183C2×C89#182812yescomplemented
184C2×C89C2×#38111yescharacteristic
185C2×#518D8911yescharacteristic
186C22×#99—892no—
187#1828—898no—
188C2×#342—894no—
189C89C2×#182811yescharacteristic, complemented, Sylow
190C23×D4C2×D8911yescharacteristic
191#518—24no—
192#518Dic8914yescomplemented
193#518C2×D8914yes—
194C2×C4×D4—24no—
195C2×#117Dic8912yescomplemented
196C22×C22⋊C4—894no—
197C22×C22⋊C4Dic8912yescomplemented
198C22×C22⋊C4C2×D8912yes—
199C2×#99—898no—
200C2×#99—1784no—
201C2×#99—1784no—
202#342—8916no—
203C25C2×Dic8911yescharacteristic
204C25C22×D8911yescharacteristic
205C22×D4—24no—
206C22×D4—24no—
207C22×D4C2×Dic8912yes—
208C22×D4C22⋊D8914yes—
209C22×D4C22⋊D8914yes—
210C22×D4C22×D8912yes—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—1784no—
214C23×C4C2×Dic8911yescharacteristic
215C4×D4—216no—
216C4×D4—216no—
217#117—24no—
218#117C2×Dic8918yescomplemented
219C2×C4⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—24no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—898no—
226C2×C22⋊C4—1784no—
227C2×C22⋊C4—1784no—
228C2×C22⋊C4—1784no—
229C2×C22⋊C4—1784no—
230C2×C22⋊C4—1784no—
231C2×C22⋊C4C2×Dic8914yes—
232C2×C22⋊C4C2×Dic8914yes—
233C2×C22⋊C4C2×Dic8918yescomplemented
234C2×C22⋊C4C22×D8914yes—
235C2×C42—22no—
236#99—17816no—
237C24—22no—
238C24—22no—
239C24—82no—
240C24—82no—
241C24C22⋊Dic8912yes—
242C24C22⋊Dic8912yes—
243C24C22×Dic8912yes—
244C24C22×Dic8911yescharacteristic
245C24C22×Dic8911yescharacteristic
246C24C2×C22⋊D8912yes—
247C24C2×C22⋊D8912yes—
248C24#1308357414yes—
249C24#1308357414yes—
250C24C23×D8911yescharacteristic
251C2×D4—28no—
252C2×D4—28no—
253C2×D4—28no—
254C2×D4—28no—
255C2×D4—28no—
256C2×D4—28no—
257C2×D4C22⋊Dic8918yes—
258C2×D4C2×C22⋊D8918yes—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—28no—
265C22×C4—84no—
266C22×C4—84no—
267C22×C4—3564no—
268C22×C4—3564no—
269C22×C4—1788no—
270C22×C4—7128no—
271C22×C4C22⋊Dic8912yes—
272C22×C4C22⋊Dic8912yes—
273C22×C4C22×Dic8912yes—
274C4⋊C4—28no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—24no—
278C22⋊C4—28no—
279C22⋊C4—3564no—
280C22⋊C4—3564no—
281C22⋊C4—1788no—
282C22⋊C4—1788no—
283C22⋊C4C22×Dic8918yes—
284C42—28no—
285C23—22no—
286C23—22no—
287C23—24no—
288C23—24no—
289C23—44no—
290C23—48no—
291C23—42no—
292C23—44no—
293C23—84no—
294C23—81no—
295C23—82no—
296C23—84no—
297C23—81no—
298C23—82no—
299C23—82no—
300C23—84no—
301C23C2×C22⋊Dic8911yescharacteristic
302C23C2×C22⋊Dic8914yes—
303C23C2×C22⋊Dic8911yescharacteristic
304C23C2×C22⋊Dic8912yes—
305C23#1566797112yes—
306C23#1566797112yes—
307C23#1566797114yes—
308C23#1566799514yes—
309C23#1566799514yes—
310C23#1566799514yes—
311C23#1566799514yes—
312C23C23×Dic8911yescharacteristic
313C23C22×C22⋊D8912yes—
314C23C2×#1308357414yes—
315D4—216no—
316D4—216no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—28no—
322C2×C4—48no—
323C2×C4—84no—
324C2×C4—84no—
325C2×C4—88no—
326C2×C4—3568no—
327C2×C4—7128no—
328C2×C4—7128no—
329C2×C4—7128no—
330C2×C4C2×C22⋊Dic8914yes—
331C22—22no—
332C22—28no—
333C22—24no—
334C22—24no—
335C22—42no—
336C22—42no—
337C22—44no—
338C22—44no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—44no—
343C22—44no—
344C22—44no—
345C22—44no—
346C22—44no—
347C22—44no—
348C22—84no—
349C22—84no—
350C22#1915146111yescharacteristic
351C22#1915146112yes—
352C22#1915146114yes—
353C22#1915146111yescharacteristic
354C22C22×C22⋊Dic8911yescharacteristic
355C22C2×#1566797112yes—
356C22C2×#1566799514yes—
357C4—24no—
358C4—48no—
359C4—7128no—
360C2—21no—
361C2—24no—
362C2—21no—
363C2—22no—
364C2—22no—
365C2—24no—
366C2—44no—
367C2#2602036012yesdirect product factor
368C2C2×#1915146111yescharacteristic
subgroupG/H
centerC22#19151461
commutatorC23×C89C23×C4
FrattiniC24C23×D89
FittingC2×#518×C89C2
socleC22×C89#381
prime radicalC23×D4×C89C22
cosocleC24×C89C24
hypercenterC2×#518D89
hypocenterC89C2×#1828
LCSG ▷ C23×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C25 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. #26020360C2direct (N × H)
3. C2×#19151364C2semidirect
9. #19151364C22semidirect
12. #518×C89C4semidirect
15. C2×#117×C89C4semidirect
16. C22×C22⋊C4×C89C4semidirect
40. #117×C89C2×C4semidirect
49. C2×C22⋊C4×C89C2×C4semidirect
183. C2×C89#1828semidirect
189. C89C2×#1828semidirect
192. #518Dic89semidirect
195. C2×#117Dic89semidirect
197. C22×C22⋊C4Dic89semidirect
218. #117C2×Dic89semidirect
233. C2×C22⋊C4C2×Dic89semidirect
367. C2#26020360direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679272
#260203602
C2×#191513642
C2×#518×C892
C2×#182889