Finite Group Databasebeta

← C2×#13072899 #14923590

Subgroups — C2×#13072899 #14923590

Order 2816.

2918 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic11⋊C4C211yesmaximal, characteristic
2#13072899C2116yesmaximal, direct product factor
3C2×#10622595C212yesmaximal, complemented
4C2×#10622593C212yesmaximal, complemented
5C2×#10622546C214yesmaximal, complemented
6C2×#10622559C212yesmaximal
7C2×#10622824C211yesmaximal, characteristic
8C2×#10622556C212yesmaximal
9C22×C11×#117C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C2×C11×#117—28no—
14C2×C11×#117C2218yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C42×C11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×Dic11⋊C4—28no—
21C22×Dic11⋊C4C2218yes—
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2214yes—
25#10622824C2218yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31#10622595C22116yescomplemented
32#10622593C22116yescomplemented
33#10622559C22116yes—
34#10622556C22116yes—
35#10622546C22132yescomplemented
36C25×C11C2311yescharacteristic
37C23×C4×C11—28no—
38C23×C4×C11D418yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2314yes—
44C23×Dic11—24no—
45C23×Dic11—28no—
46C23×Dic11—24no—
47C23×Dic11—28no—
48C23×Dic11C2314yes—
49C23×Dic11C2314yes—
50C23×Dic11C2312yes—
51C23×Dic11C2314yes—
52C23×Dic11C2312yes—
53C11×#117—232no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4C2314yes—
57C2×C11×C4⋊C4C2314yes—
58C2×C11×C22⋊C4—28no—
59C2×C11×C22⋊C4C2318yes—
60C2×C42×C11—28no—
61C2×C42×C11C2318yes—
62C2×C22⋊Dic11—28no—
63C2×C22⋊Dic11C2318yes—
64C2×Dic11⋊C4—28no—
65C2×Dic11⋊C4—28no—
66C2×Dic11⋊C4—232no—
67C2×Dic11⋊C4—216no—
68C2×Dic11⋊C4C2318yes—
69C2×Dic11⋊C4C23116yes—
70C2×Dic11⋊C4C2318yes—
71C11⋊#95C2318yes—
72C11⋊#95C23116yes—
73C11⋊#95C23116yes—
74C11⋊#95C23116yes—
75C11⋊#95C2318yes—
76C2×#2484—111nomaximal, Sylow
77C24×C11—24no—
78C24×C11—24no—
79C24×C11C2×D414yes—
80C24×C11#4118yes—
81C24×C11C2412yes—
82C24×C11C2411yescharacteristic
83C22×C4×C11—232no—
84C22×C4×C11—216no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—28no—
90C22×C4×C11—28no—
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2×D414yes—
93C22×C4×C11C2×D4116yes—
94C22×C4×C11C2414yes—
95C22×C4×C11C2414yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2412yes—
98C22×Dic11—232no—
99C22×Dic11—216no—
100C22×Dic11—28no—
101C22×Dic11—24no—
102C22×Dic11—28no—
103C22×Dic11—24no—
104C22×Dic11—24no—
105C22×Dic11—28no—
106C22×Dic11—28no—
107C22×Dic11—216no—
108C22×Dic11—28no—
109C22×Dic11—28no—
110C22×Dic11—416no—
111C22×Dic11#4118yes—
112C22×Dic11C2418yes—
113C22×Dic11C2414yes—
114C22×Dic11C2414yes—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—28no—
117C11×C22⋊C4—216no—
118C42×C11—216no—
119C22⋊Dic11—216no—
120Dic11⋊C4—232no—
121Dic11⋊C4—216no—
122Dic11⋊C4—216no—
123C22×#117D1111yescharacteristic
124C23×C4⋊C4—111no—
125#2484—1116no—
126C2×#400—112no—
127C2×#398—112no—
128C2×#387—114no—
129C2×#385—112no—
130C2×#381—111no—
131C2×#381—112no—
132C23×C11—28no—
133C23×C11—28no—
134C23×C11—232no—
135C23×C11—24no—
136C23×C11—24no—
137C23×C11#123116yes—
138C23×C11C22×D414yes—
139C23×C11C22×D412yes—
140C23×C11C2×#4118yes—
141C23×C11C2×#4114yes—
142C23×C11C2×#4114yes—
143C23×C112−1+414yes—
144C23×C11C2511yescharacteristic
145C2×C4×C11—232no—
146C2×C4×C11—28no—
147C2×C4×C11—28no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—28no—
153C2×C4×C11—28no—
154C2×C4×C11—48no—
155C2×C4×C11—48no—
156C2×C4×C11C22×D414yes—
157C2×C4×C11C22×D414yes—
158C2×Dic11—232no—
159C2×Dic11—216no—
160C2×Dic11—24no—
161C2×Dic11—24no—
162C2×Dic11—24no—
163C2×Dic11—28no—
164C2×Dic11—28no—
165C2×Dic11—28no—
166C2×Dic11—28no—
167C2×Dic11—416no—
168C2×Dic11—48no—
169C2×Dic11—416no—
170C2×Dic11C2×#4118yes—
171C24×C4—111no—
172C24×C4—111no—
173C24×C4C2×D1111yescharacteristic
174C2×#117—28no—
175C2×#117C2×D1118yes—
176C22×C4⋊C4—112no—
177C22×C4⋊C4—114no—
178C22×C4⋊C4—118no—
179C22×C4⋊C4—112no—
180C22×C4⋊C4—228no—
181C22×C4⋊C4C2×D1111yescharacteristic
182C22×C4⋊C4C2×D1111yescharacteristic
183C22×C22⋊C4—112no—
184C22×C22⋊C4C2×D1112yes—
185C22×C42C2×D1112yes—
186#400—1116no—
187#398—1116no—
188#387—1132no—
189#385—1116no—
190#381—118no—
191#381—1116no—
192C2×#95—112no—
193C2×#95—114no—
194C2×#95—114no—
195C2×#95—114no—
196C2×#95—112no—
197C22×C11—24no—
198C22×C11—24no—
199C22×C11—216no—
200C22×C11—232no—
201C22×C11C2×#12318yes—
202C22×C11C2×#12314yes—
203C22×C11#52514yes—
204C22×C11#53614yes—
205C22×C11#552116yes—
206C22×C11C23×D411yescharacteristic
207C22×C11C22×#4112yes—
208C22×C11C22×#4112yes—
209C22×C11C2×2−1+412yes—
210C4×C11—24no—
211C4×C11—24no—
212C4×C11—44no—
213C4×C11—44no—
214Dic11—28no—
215Dic11—44no—
216Dic11—48no—
217C25C22×D1111yescharacteristic
218C23×C4—28no—
219C23×C4—112no—
220C23×C4—114no—
221C23×C4—114no—
222C23×C4—114no—
223C23×C4—112no—
224C23×C4—228no—
225C23×C4—224no—
226C23×C4—228no—
227C23×C4—224no—
228C23×C4C22⋊D1118yes—
229C23×C4C22×D1112yes—
230C23×C4C22×D1112yes—
231C23×C4C22×D1114yes—
232C23×C4C22×D1111yescharacteristic
233C23×C4C22×D1111yescharacteristic
234#117—232no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—118no—
238C2×C4⋊C4—118no—
239C2×C4⋊C4—1116no—
240C2×C4⋊C4—2216no—
241C2×C4⋊C4—228no—
242C2×C4⋊C4—228no—
243C2×C4⋊C4—2232no—
244C2×C4⋊C4C22×D1114yes—
245C2×C4⋊C4C22×D1114yes—
246C2×C22⋊C4—28no—
247C2×C22⋊C4—118no—
248C2×C22⋊C4—228no—
249C2×C22⋊C4C22×D1118yes—
250C2×C42—28no—
251C2×C42C22×D1118yes—
252#95—118no—
253#95—1116no—
254#95—1116no—
255#95—118no—
256#95—1116no—
257C2×C11—28no—
258C2×C11#248418yescomplemented
259C2×C11C22×#12311yescharacteristic
260C2×C11C2×#52511yescharacteristic
261C2×C11C2×#53611yescharacteristic
262C2×C11C2×#55214yes—
263C24—24no—
264C24—24no—
265C24#433918yes—
266C24C2×C22⋊D1114yes—
267C24C23×D1112yes—
268C24C23×D1111yescharacteristic
269C22×C4—232no—
270C22×C4—216no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—28no—
274C22×C4—28no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—118no—
278C22×C4—114no—
279C22×C4—118no—
280C22×C4—114no—
281C22×C4—2216no—
282C22×C4—2232no—
283C22×C4—224no—
284C22×C4—228no—
285C22×C4—224no—
286C22×C4—228no—
287C22×C4—2216no—
288C22×C4—228no—
289C22×C4—228no—
290C22×C4—228no—
291C22×C4—228no—
292C22×C4—224no—
293C22×C4—4416no—
294C22×C4C2×C22⋊D1114yes—
295C22×C4C2×C22⋊D1114yes—
296C22×C4C2×C22⋊D11116yes—
297C22×C4C23×D1114yes—
298C22×C4C23×D1114yes—
299C22×C4C23×D1112yes—
300C22×C4C23×D1112yes—
301C4⋊C4—28no—
302C4⋊C4—28no—
303C4⋊C4—2232no—
304C4⋊C4—2216no—
305C4⋊C4—2216no—
306C22⋊C4—216no—
307C22⋊C4—2216no—
308C42—216no—
309C11C2×#248411yescharacteristic, complemented, Sylow
310C23—232no—
311C23—28no—
312C23—28no—
313C23—24no—
314C23—24no—
315C23#66982116yes—
316C23C2×#433918yes—
317C23C2×#433914yes—
318C23#41×D1114yes—
319C23#6704314yes—
320C23C22×C22⋊D1114yes—
321C23C22×C22⋊D1112yes—
322C23C24×D1111yescharacteristic
323C2×C4—232no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—48no—
333C2×C4—48no—
334C2×C4—118no—
335C2×C4—2232no—
336C2×C4—2216no—
337C2×C4—224no—
338C2×C4—224no—
339C2×C4—228no—
340C2×C4—228no—
341C2×C4—228no—
342C2×C4—228no—
343C2×C4—224no—
344C2×C4—4416no—
345C2×C4—4416no—
346C2×C4—448no—
347C2×C4C22×C22⋊D1114yes—
348C2×C4C22×C22⋊D1114yes—
349C22—232no—
350C22—216no—
351C22—24no—
352C22—24no—
353C22#10623062116yes—
354C22C2×#6698218yes—
355C22C2×#6698214yes—
356C22#1062335614yes—
357C22#1062335914yes—
358C22C22×#433912yes—
359C22C2×#41×D1112yes—
360C22C2×#6704312yes—
361C22C23×C22⋊D1111yescharacteristic
362C4—24no—
363C4—24no—
364C4—44no—
365C4—44no—
366C4—228no—
367C4—448no—
368C4—444no—
369C2—28no—
370C2#1307289918yesdirect product factor
371C2C22×#6698211yescharacteristic
372C2C2×#1062335911yescharacteristic
373C2C2×#1062335611yescharacteristic
374C2C2×#1062306214yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#117C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#117D11
hypocenterC11C2×#2484
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #13072899C2direct (N × H)
3. C2×#10622595C2semidirect
4. C2×#10622593C2semidirect
5. C2×#10622546C2semidirect
31. #10622595C22semidirect
32. #10622593C22semidirect
35. #10622546C22semidirect
258. C2×C11#2484semidirect
309. C11C2×#2484semidirect
370. C2#13072899direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
#130728992
C2×#106225952
C2×#106225932
C2×#106225462
C2×#106225592
C2×#106228242
C2×#106225562
C22×C11×#1172
C2×#248411