Finite Group Databasebeta

← C2×#13074446 #14920840

Subgroups — C2×#13074446 #14920840

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic, complemented
2#13074446C2116yesmaximal, direct product factor
3C2×#10622597C214yesmaximal, complemented
4C2×#10622561C214yesmaximal
5C2×#10622541C212yesmaximal, complemented
6C2×#10622548C211yesmaximal, characteristic, complemented
7C2×#10622825C212yesmaximal
8C22×C11×#117C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C2×C11×#117—28no—
11C2×C11×#117C2218yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C22⋊Dic11C2214yes—
17C22×C4⋊Dic11C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4⋊Dic11C2214yes—
20C22×Dic11⋊C4C2214yes—
21C22×Dic11⋊C4C2214yes—
22C2×#66923—28no—
23C2×#66923C2218yescomplemented
24#10622825C22116yes—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27#10622597C22132yescomplemented
28#10622561C22132yes—
29#10622548C2218yescomplemented
30#10622541C22116yescomplemented
31C25×C11C2311yescharacteristic
32C23×C4×C11—24no—
33C23×C4×C11—24no—
34C23×C4×C11Q818yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2314yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2314yes—
41C23×Dic11C2314yes—
42C11×#117—232no—
43C2×C11×C4⋊C4—28no—
44C2×C11×C4⋊C4C2318yes—
45C2×C11×C22⋊C4—28no—
46C2×C11×C22⋊C4C2318yes—
47C2×C42×C11—24no—
48C2×C42×C11D418yes—
49C2×C42×C11C2314yes—
50C2×C42×C11C2314yes—
51C2×C22⋊Dic11—48no—
52C2×C22⋊Dic11C23116yes—
53C2×C4⋊Dic11—28no—
54C2×C4⋊Dic11—28no—
55C2×C4⋊Dic11—48no—
56C2×C4⋊Dic11C2318yes—
57C2×C4⋊Dic11C2318yes—
58C2×C4⋊Dic11C23116yes—
59C2×Dic11⋊C4—216no—
60C2×Dic11⋊C4—48no—
61C2×Dic11⋊C4C23116yes—
62C2×Dic11⋊C4C23116yes—
63#66923—232no—
64C11⋊#95C23116yes—
65C11⋊#95C23116yes—
66C2×#2629—111nomaximal, Sylow
67C24×C11—22no—
68C24×C11—22no—
69C24×C11—24no—
70C24×C11—24no—
71C24×C11C2×Q814yes—
72C24×C11C2412yes—
73C24×C11C2411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—232no—
79C22×C4×C11—28no—
80C22×C4×C11—28no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11C2×D418yes—
85C22×C4×C11C2×D414yes—
86C22×C4×C11C2×Q814yes—
87C22×C4×C11C2×Q8116yes—
88C22×C4×C11C2×Q814yes—
89C22×C4×C11#4114yes—
90C22×C4×C11C2414yes—
91C22×C4×C11C2414yes—
92C22×C4×C11C2412yes—
93C22×C4×C11C2412yes—
94C22×Dic11—28no—
95C22×Dic11—28no—
96C22×Dic11—28no—
97C22×Dic11—28no—
98C22×Dic11—28no—
99C22×Dic11—28no—
100C22×Dic11C2418yes—
101C22×Dic11C2418yes—
102C11×C4⋊C4—216no—
103C11×C22⋊C4—216no—
104C42×C11—28no—
105C42×C11C2×D4116yes—
106C22⋊Dic11—416no—
107C4⋊Dic11—216no—
108C4⋊Dic11—216no—
109C4⋊Dic11—416no—
110Dic11⋊C4—232no—
111Dic11⋊C4—416no—
112C22×#125—111no—
113C22×#117D1111yescharacteristic
114#2629—1116no—
115C2×#398—114no—
116C2×#396—114no—
117C2×#389—112no—
118C2×#384—111no—
119C2×#380—112no—
120C23×C11—28no—
121C23×C11—216no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—24no—
125C23×C11—24no—
126C23×C11—48no—
127C23×C11—44no—
128C23×C11—44no—
129C23×C11C22×D412yes—
130C23×C11C22×Q814yes—
131C23×C11C22×Q812yes—
132C23×C11C2×#4112yes—
133C23×C11H(5,𝔽2)14yes—
134C23×C112−1+414yes—
135C23×C11C2511yescharacteristic
136C2×C4×C11—28no—
137C2×C4×C11—216no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—232no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—48no—
147C2×C4×C11C22⋊Q8116yes—
148C2×C4×C11C22×D418yes—
149C2×C4×C11C22×D414yes—
150C2×C4×C11C22×Q814yes—
151C2×C4×C11C22×Q814yes—
152C2×C4×C11C2×#4114yes—
153C2×Dic11—28no—
154C2×Dic11—28no—
155C2×Dic11—28no—
156C2×Dic11—28no—
157C2×Dic11—28no—
158C2×Dic11—28no—
159C2×Dic11—416no—
160C2×Dic11—416no—
161C24×C4C2×D1111yescharacteristic
162C2×#125—118no—
163C2×#125—228no—
164C2×#117—28no—
165C2×#117C2×D1118yes—
166C22×C4⋊C4—114no—
167C22×C4⋊C4—112no—
168C22×C4⋊C4—112no—
169C22×C4⋊C4—114no—
170C22×C4⋊C4—114no—
171C22×C4⋊C4C2×D1112yes—
172C22×C22⋊C4—114no—
173C22×C22⋊C4C2×D1112yes—
174C22×C42C2×D1111yescharacteristic
175C22×C42C2×D1111yescharacteristic
176#398—1132no—
177#396—1132no—
178#389—1116no—
179#384—118no—
180#380—1116no—
181C2×#95—114no—
182C2×#95—114no—
183C22×C11—24no—
184C22×C11—28no—
185C22×C11—416no—
186C22×C11—44no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11C2×C22⋊Q814yes—
190C22×C11#53718yes—
191C22×C11#54014yes—
192C22×C11#54114yes—
193C22×C11#54418yes—
194C22×C11C23×D411yescharacteristic
195C22×C11C23×Q811yescharacteristic
196C22×C11C22×#4111yescharacteristic
197C22×C11C2×H(5,𝔽2)12yes—
198C22×C11C2×2−1+412yes—
199C4×C11—24no—
200C4×C11—28no—
201C4×C11—44no—
202C4×C11C2×C22⋊Q818yes—
203Dic11—48no—
204Dic11—48no—
205C25C22×D1111yescharacteristic
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—114no—
209C23×C4—114no—
210C23×C4Dic2218yes—
211C23×C4C22×D1112yes—
212C23×C4C22×D1114yes—
213C23×C4C22×D1111yescharacteristic
214C23×C4C22×D1112yes—
215C23×C4C22×D1111yescharacteristic
216#125—2232no—
217#117—232no—
218C2×C4⋊C4—28no—
219C2×C4⋊C4—118no—
220C2×C4⋊C4—1116no—
221C2×C4⋊C4—118no—
222C2×C4⋊C4—1116no—
223C2×C4⋊C4—1116no—
224C2×C4⋊C4—228no—
225C2×C4⋊C4—2216no—
226C2×C4⋊C4—228no—
227C2×C4⋊C4—448no—
228C2×C4⋊C4—448no—
229C2×C4⋊C4C22×D1118yes—
230C2×C22⋊C4—28no—
231C2×C22⋊C4—1116no—
232C2×C22⋊C4—448no—
233C2×C22⋊C4C22×D1118yes—
234C2×C42—24no—
235C2×C42C22⋊D1118yes—
236C2×C42C22×D1114yes—
237C2×C42C22×D1114yes—
238#95—1116no—
239#95—1116no—
240C2×C11—44no—
241C2×C11#262918yescomplemented
242C2×C11C22×C22⋊Q811yescharacteristic
243C2×C11C2×#53712yes—
244C2×C11C2×#54011yescharacteristic
245C2×C11C2×#54111yescharacteristic
246C2×C11C2×#54412yes—
247C24—22no—
248C24—24no—
249C24—24no—
250C24—22no—
251C24C2×Dic2214yes—
252C24C23×D1112yes—
253C24C23×D1111yescharacteristic
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—232no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—118no—
265C22×C4—118no—
266C22×C4—228no—
267C22×C4—228no—
268C22×C4—228no—
269C22×C4—228no—
270C22×C4—228no—
271C22×C4—228no—
272C22×C4C2×Dic2214yes—
273C22×C4C2×Dic22116yes—
274C22×C4C2×Dic2214yes—
275C22×C4#433914yes—
276C22×C4C2×C22⋊D1118yes—
277C22×C4C2×C22⋊D1114yes—
278C22×C4C23×D1114yes—
279C22×C4C23×D1112yes—
280C22×C4C23×D1114yes—
281C22×C4C23×D1112yes—
282C4⋊C4—216no—
283C4⋊C4—2216no—
284C4⋊C4—2232no—
285C4⋊C4—2216no—
286C4⋊C4—4416no—
287C4⋊C4—4416no—
288C22⋊C4—216no—
289C22⋊C4—4416no—
290C42—28no—
291C42C2×C22⋊D11116yes—
292C11C2×#262911yescharacteristic, complemented, Sylow
293C23—216no—
294C23—28no—
295C23—22no—
296C23—24no—
297C23—24no—
298C23—22no—
299C23—44no—
300C23—44no—
301C23—48no—
302C23C22×Dic2214yes—
303C23C22×Dic2212yes—
304C23C2×#433912yes—
305C23#6704214yes—
306C23#6704314yes—
307C23C22×C22⋊D1112yes—
308C23C24×D1111yescharacteristic
309C2×C4—28no—
310C2×C4—216no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—232no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—48no—
320C2×C4—228no—
321C2×C4—228no—
322C2×C4—228no—
323C2×C4—228no—
324C2×C4—228no—
325C2×C4—228no—
326C2×C4—4416no—
327C2×C4—4416no—
328C2×C4#66977116yes—
329C2×C4C22×Dic2214yes—
330C2×C4C22×Dic2214yes—
331C2×C4C2×#433914yes—
332C2×C4C22×C22⋊D1118yes—
333C2×C4C22×C22⋊D1114yes—
334C22—28no—
335C22—24no—
336C22—416no—
337C22—44no—
338C22—42no—
339C22—42no—
340C22#1062304914yes—
341C22#1062305018yes—
342C22#1062306614yes—
343C22C2×#6697714yes—
344C22#1062336418yes—
345C22C23×Dic2211yescharacteristic
346C22C22×#433911yescharacteristic
347C22C2×#6704212yes—
348C22C2×#6704312yes—
349C22C23×C22⋊D1111yescharacteristic
350C4—28no—
351C4—24no—
352C4—44no—
353C4—448no—
354C4—448no—
355C4C2×#6697718yes—
356C2—44no—
357C2#1307444618yesdirect product factor
358C2C22×#6697711yescharacteristic
359C2C2×#1062336412yes—
360C2C2×#1062306611yescharacteristic
361C2C2×#1062304911yescharacteristic
362C2C2×#1062305012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#117C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#117D11
hypocenterC11C2×#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#66923C2semidirect
2. #13074446C2direct (N × H)
3. C2×#10622597C2semidirect
5. C2×#10622541C2semidirect
6. C2×#10622548C2semidirect
23. C2×#66923C22semidirect
27. #10622597C22semidirect
29. #10622548C22semidirect
30. #10622541C22semidirect
241. C2×C11#2629semidirect
292. C11C2×#2629semidirect
357. C2#13074446direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
#130744462
C2×#106225972
C2×#106225612
C2×#106225412
C2×#106225482
C2×#106228252
C22×C11×#1172
C2×#262911