Finite Group Databasebeta

← C2×#13070039 #14782592

Subgroups — C2×#13070039 #14782592

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66882C211yesmaximal, characteristic, complemented
2C2×#10622825C212yesmaximal
3#13070039C218yesmaximal, direct product factor
4C2×#10622189C211yesmaximal, characteristic, complemented
5C2×#10622189C212yesmaximal, complemented
6C22×C11×C22⋊C8C211yesmaximal, characteristic
7C24×C4×C11C2211yescharacteristic
8C23×C8×C11C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C22×C22⋊Dic11—22no—
11C22×C4⋊Dic11C2212yes—
12C22×C4⋊Dic11C2212yes—
13C2×C11×C22⋊C8—24no—
14C2×C11×C22⋊C8C2214yes—
15#10622825—24no—
16#10622825C2218yes—
17C2×C11⋊#95—22no—
18C2×#66882—24no—
19C2×#66882C2214yescomplemented
20#10622189C2214yescomplemented
21#10622189C2218yescomplemented
22C25×C11D411yescharacteristic
23C23×C4×C11—22no—
24C23×C4×C11—22no—
25C23×C4×C11—24no—
26C23×C4×C11—24no—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D412yes—
29C23×C4×C11C2312yes—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—22no—
32C23×Dic11—22no—
33C22×C8×C11—24no—
34C22×C8×C11—22no—
35C22×C8×C11—24no—
36C22×C8×C11D414yes—
37C22×C8×C11C2312yes—
38C22×C8×C11C2312yes—
39C2×C22⋊Dic11—28no—
40C2×C22⋊Dic11—48no—
41C2×C4⋊Dic11—24no—
42C2×C4⋊Dic11—24no—
43C2×C4⋊Dic11—24no—
44C2×C4⋊Dic11—24no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11C2314yes—
48C2×C4⋊Dic11C2314yes—
49C11×C22⋊C8—28no—
50C11⋊#95—28no—
51#66882—28no—
52C2×#2075—111nomaximal, Sylow
53C24×C11—22no—
54C24×C11—24no—
55C24×C11—22no—
56C24×C11—24no—
57C24×C11D814yes—
58C24×C11C2×D412yes—
59C24×C11C2×D411yescharacteristic
60C22×C4×C11—22no—
61C22×C4×C11—24no—
62C22×C4×C11—24no—
63C22×C4×C11—28no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—44no—
69C22×C4×C11—44no—
70C22×C4×C11—48no—
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11#4112yes—
75C22×C4×C11#4114yes—
76C22×C4×C11#4114yes—
77C22×C4×C11C2411yescharacteristic
78C22×Dic11—24no—
79C22×Dic11—24no—
80C22×Dic11—44no—
81C22×Dic11—44no—
82C22×Dic11—44no—
83C22×Dic11—44no—
84C22×Dic11—44no—
85C22×Dic11—44no—
86C2×C8×C11—28no—
87C2×C8×C11—22no—
88C2×C8×C11—24no—
89C2×C8×C11—24no—
90C2×C8×C11—44no—
91C2×C8×C11C2×D414yes—
92C22⋊Dic11—416no—
93C4⋊Dic11—24no—
94C4⋊Dic11—24no—
95C4⋊Dic11—24no—
96C4⋊Dic11—24no—
97C4⋊Dic11—44no—
98C4⋊Dic11—44no—
99C22×#107—111no—
100C22×C22⋊C8D1111yescharacteristic
101C2×#380—112no—
102#2075—118no—
103C2×#340—112no—
104C2×#340—111no—
105C23×C11—22no—
106C23×C11—24no—
107C23×C11—22no—
108C23×C11—24no—
109C23×C11—28no—
110C23×C11—216no—
111C23×C11—44no—
112C23×C11—44no—
113C23×C11—48no—
114C23×C11#12112yes—
115C23×C11#12314yes—
116C23×C11C2×D814yes—
117C23×C11C2×D812yes—
118C23×C11#13512yes—
119C23×C11#13714yes—
120C23×C11C22×D411yescharacteristic
121C2×C4×C11—22no—
122C2×C4×C11—24no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—48no—
128C2×C4×C11#12112yes—
129C2×C4×C11#12314yes—
130C2×C4×C11#12314yes—
131C2×C4×C11#12414yes—
132C2×C4×C11#12618yes—
133C2×C4×C11C22×D411yescharacteristic
134C2×C4×C11C2×#4111yescharacteristic
135C2×C4×C11C2×#4112yes—
136C2×C4×C11C2×#4112yes—
137C2×Dic11—44no—
138C2×Dic11—44no—
139C2×Dic11—44no—
140C2×Dic11—44no—
141C2×Dic11—44no—
142C2×Dic11—44no—
143C2×Dic11—88no—
144C2×Dic11—88no—
145C8×C11—24no—
146C8×C11—42no—
147C24×C4C2×D1111yescharacteristic
148C23×C8C2×D1111yescharacteristic
149C23×C8C2×D1111yescharacteristic
150C22×C4⋊C4—112no—
151C22×C4⋊C4—112no—
152C22×C22⋊C4—222no—
153C2×#107—114no—
154C2×#107—224no—
155C2×C22⋊C8—24no—
156C2×C22⋊C8C2×D1114yes—
157#380—118no—
158#380—224no—
159C2×#95—222no—
160#340—114no—
161#340—118no—
162C22×C11—28no—
163C22×C11—24no—
164C22×C11—44no—
165C22×C11—416no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11#39714yes—
169C22×C11#46614yes—
170C22×C11#47014yes—
171C22×C11#48018yes—
172C22×C11#48518yes—
173C22×C11C2×#12111yescharacteristic
174C22×C11C2×#12312yes—
175C22×C11C22×D811yescharacteristic
176C22×C11C2×#13511yescharacteristic
177C22×C11C2×#13712yes—
178C4×C11—42no—
179C4×C11#39714yes—
180C4×C11C2×#12311yescharacteristic
181C4×C11C2×#12411yescharacteristic
182C4×C11C2×#12612yes—
183Dic11—84no—
184Dic11—84no—
185C25D4411yescharacteristic
186C23×C4—22no—
187C23×C4—24no—
188C23×C4—24no—
189C23×C4—22no—
190C23×C4—222no—
191C23×C4—222no—
192C23×C4D4412yes—
193C23×C4D4411yescharacteristic
194C23×C4C22×D1112yes—
195C23×C4C22×D1111yescharacteristic
196C22×C8—24no—
197C22×C8—24no—
198C22×C8—22no—
199C22×C8C22⋊D1114yes—
200C22×C8C22×D1112yes—
201C22×C8C22×D1112yes—
202C2×C4⋊C4—114no—
203C2×C4⋊C4—114no—
204C2×C4⋊C4—224no—
205C2×C4⋊C4—224no—
206C2×C4⋊C4—224no—
207C2×C4⋊C4—224no—
208C2×C4⋊C4—222no—
209C2×C4⋊C4—222no—
210C2×C22⋊C4—228no—
211C2×C22⋊C4—448no—
212#107—228no—
213C22⋊C8—28no—
214#95—228no—
215C2×C11—44no—
216C2×C11#207518yescomplemented
217C2×C11C2×#39711yescharacteristic
218C2×C11C2×#46611yescharacteristic
219C2×C11C2×#47011yescharacteristic
220C2×C11C2×#48012yes—
221C2×C11C2×#48512yes—
222C24—24no—
223C24—22no—
224C24—24no—
225C24—22no—
226C24D8814yes—
227C24C2×D4412yes—
228C24C2×D4411yescharacteristic
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—28no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—22no—
237C22×C4—48no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—224no—
241C22×C4—224no—
242C22×C4—444no—
243C22×C4—444no—
244C22×C4—444no—
245C22×C4—444no—
246C22×C4—444no—
247C22×C4—444no—
248C22×C4C2×D4412yes—
249C22×C4C2×D4411yescharacteristic
250C22×C4#433912yes—
251C22×C4#434114yes—
252C22×C4#434114yes—
253C22×C4C2×C22⋊D1112yes—
254C22×C4C23×D1111yescharacteristic
255C2×C8—28no—
256C2×C8—24no—
257C2×C8—24no—
258C2×C8—22no—
259C2×C8—44no—
260C2×C8C2×C22⋊D1114yes—
261C4⋊C4—224no—
262C4⋊C4—224no—
263C4⋊C4—224no—
264C4⋊C4—224no—
265C4⋊C4—444no—
266C4⋊C4—444no—
267C22⋊C4—4416no—
268C11C2×#207511yescharacteristic, complemented, Sylow
269C23—28no—
270C23—22no—
271C23—24no—
272C23—24no—
273C23—22no—
274C23—216no—
275C23—44no—
276C23—44no—
277C23—48no—
278C23#6693914yes—
279C23C2×D8814yes—
280C23C2×D8812yes—
281C23#6695712yes—
282C23#6696214yes—
283C23#6698312yes—
284C23C22×D4411yescharacteristic
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—48no—
292C2×C4—444no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4—444no—
296C2×C4—444no—
297C2×C4—444no—
298C2×C4—888no—
299C2×C4—888no—
300C2×C4#6693218yes—
301C2×C4#6693914yes—
302C2×C4#6698312yes—
303C2×C4#6698814yes—
304C2×C4#6698914yes—
305C2×C4C2×#433911yescharacteristic
306C2×C4C2×#434112yes—
307C2×C4C2×#434112yes—
308C2×C4C22×C22⋊D1111yescharacteristic
309C8—24no—
310C8—42no—
311C22—24no—
312C22—28no—
313C22—42no—
314C22—416no—
315C22—42no—
316C22—44no—
317C22#1062233618yes—
318C22#1062234918yes—
319C22#1062256614yes—
320C22#1062272814yes—
321C22#1062275014yes—
322C22C2×#6693912yes—
323C22C22×D8811yescharacteristic
324C22C2×#6695711yescharacteristic
325C22C2×#6696212yes—
326C22C2×#6698311yescharacteristic
327C4—42no—
328C4—884no—
329C4—884no—
330C4#1062256614yes—
331C4C2×#6693212yes—
332C4C2×#6698811yescharacteristic
333C4C2×#6698911yescharacteristic
334C2—44no—
335C2#1307003918yesdirect product factor
336C2C2×#1062256611yescharacteristic
337C2C2×#1062272811yescharacteristic
338C2C2×#1062275011yescharacteristic
339C2C2×#1062234912yes—
340C2C2×#1062233612yes—
subgroupG/H
centerC24C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊C8C2
socleC24×C11C2×D4
prime radicalC25×C11D4
hypercenterC22×C22⋊C8D11
hypocenterC11C2×#2075
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#66882C2semidirect
3. #13070039C2direct (N × H)
4. C2×#10622189C2semidirect
5. C2×#10622189C2semidirect
19. C2×#66882C22semidirect
20. #10622189C22semidirect
21. #10622189C22semidirect
216. C2×C11#2075semidirect
268. C11C2×#2075semidirect
335. C2#13070039direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668822
C2×#106228252
#130700392
C2×#106221892
C22×C11×C22⋊C82
C2×#207511