Finite Group Databasebeta

← C2×#13081593 #15634670

Subgroups — C2×#13081593 #15634670

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic
2#13081593C2116yesmaximal, direct product factor
3C2×#10622698C213yesmaximal, complemented
4C2×#10622640C213yesmaximal, complemented
5C2×#10622696C213yesmaximal, complemented
6C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
7C2×C4×#4325C213yesmaximal, complemented
8C2×C11×#557C211yesmaximal, characteristic, complemented
9C22×#4343—21no—
10C11×#557—24no—
11C11×#557C2218yescomplemented
12C2×C11×C4⋊Q8C2213yes—
13C2×C11×#125—23no—
14C2×C4×Q8×C11—21no—
15C2×C4×Q8×C11C2213yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C22×#4325C2213yes—
18C22×#4325C2216yes—
19#10623108—24no—
20#10623108C2218yes—
21C2×#66948—23no—
22C2×#66927C2213yes—
23C2×C4×D44C2213yes—
24C2×#66899C2213yes—
25#10622698C22124yescomplemented
26#10622696C22124yescomplemented
27#10622640C22124yescomplemented
28C4×#4325C22124yescomplemented
29Q8×C11⋊C8C2218yescomplemented
30C2×#66873C2213yes—
31C2×#66872C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2213yes—
33C2×C4×C11⋊C8C2213yes—
34C22×Q8×C11D411yescharacteristic
35C22×Q8×C11C2313yes—
36C2×#4343—28no—
37C2×#4343—48no—
38C22×D44—23no—
39C22×D44—23no—
40C22×D44C2313yes—
41C22×C4×D11—23no—
42C11×C4⋊Q8—26no—
43C11×C4⋊Q8C23112yes—
44C11×#125—224no—
45C4×Q8×C11—28no—
46C4×Q8×C11—26no—
47C4×Q8×C11D414yes—
48C4×Q8×C11C23112yes—
49C4×Q8×C11C2314yes—
50C2×C11×C4⋊C4—23no—
51C2×C11×C4⋊C4—23no—
52C2×C11×C4⋊C4—23no—
53C2×C11×C4⋊C4D413yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11—23no—
56C2×C42×C11C2313yes—
57C2×#4325—212no—
58C2×#4325—412no—
59C2×#4325C23112yes—
60C2×#4325C23124yes—
61C2×(C2×D11)⋊C4—23no—
62C2×C4⋊Dic11C2311yescharacteristic
63C22×C11⋊C8C2313yes—
64C22×C11⋊C8C2311yescharacteristic
65#66948—224no—
66#66927—26no—
67#66927C23112yes—
68C4×D44—26no—
69C4×D44C23112yes—
70#66899C23112yes—
71#66873C23112yes—
72#66872C2314yes—
73C4⋊(C11⋊C8)C23112yes—
74C4×C11⋊C8C23112yes—
75C2×#3392—111nomaximal, Sylow
76C23×D11—23no—
77C2×Q8×C11—23no—
78C2×Q8×C11—26no—
79C2×Q8×C11—26no—
80C2×Q8×C11SD1618yescomplemented
81C2×Q8×C11C2×D414yes—
82C2×Q8×C11C2416yes—
83C22×C4×C11—21no—
84C22×C4×C11—23no—
85C22×C4×C11C2×D413yes—
86C22×C4×C11C2×D413yes—
87C22×C4×C11C2411yescharacteristic
88C22×Dic11—21no—
89#4343—432no—
90C2×D44—23no—
91C2×D44—212no—
92C2×D44—212no—
93C2×D44—26no—
94C2×D44—26no—
95C2×D44—412no—
96C2×D44—86no—
97C2×D44C2416yes—
98C2×C4×D11—212no—
99C2×C4×D11—412no—
100C11×C4⋊C4—212no—
101C11×C4⋊C4—212no—
102C11×C4⋊C4—212no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4C2×D4112yes—
105C11×C4⋊C4C2412yes—
106C42×C11—212no—
107C42×C11C2×D416yes—
108C42×C11C2416yes—
109#4325—224no—
110#4325—424no—
111(C2×D11)⋊C4—212no—
112C4⋊Dic11—21no—
113C4⋊Dic11C2412yes—
114C2×C11⋊C8—26no—
115C2×C11⋊C8#4114yescomplemented
116C2×C11⋊C8C2416yes—
117C2×C11⋊C8C2412yes—
118C2×#557D1111yescharacteristic, complemented
119C2×#550—111no—
120#3392—1116no—
121C2×#492—113no—
122C2×#460—113no—
123C2×#461—113no—
124C2×C8×Q8—111no—
125C2×C4×SD16—113no—
126C23×C11C22×D411yescharacteristic
127C22×D11—26no—
128C22×D11—46no—
129C22×D11—46no—
130C22×D11—46no—
131Q8×C11—26no—
132Q8×C11—26no—
133Q8×C11—46no—
134Q8×C11C2×SD16116yescomplemented
135C2×C4×C11—26no—
136C2×C4×C11—22no—
137C2×C4×C11—26no—
138C2×C4×C11—46no—
139C2×C4×C11—42no—
140C2×C4×C11C2×SD16112yes—
141C2×C4×C11C22×D416yes—
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×D416yes—
144C2×C4×C11C2×#4112yes—
145C2×C4×C11H(5,𝔽2)12yes—
146C2×C4×C11C2511yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—42no—
149D44—26no—
150D44—26no—
151D44—46no—
152D44—424no—
153D44—812no—
154C4×D11—424no—
155C11⋊C8—26no—
156C11⋊C8C2×#4114yescomplemented
157C22×#41—221no—
158C22×SD16—113no—
159C22×SD16—116no—
160#557—24no—
161#557C2×D1118yescomplemented
162#550—118no—
163#550—224no—
164C2×C4⋊Q8C2×D1113yes—
165C2×#127—113no—
166C2×#125—23no—
167C2×#121—223no—
168C2×C4×Q8—21no—
169C2×C4×Q8C2×D1113yes—
170C2×C4×Q8C2×D1111yescharacteristic
171C2×C4×D4—113no—
172#492—1124no—
173#461—1124no—
174#460—1124no—
175C8×Q8—118no—
176C4×SD16—1124no—
177C2×#106—111no—
178C2×C4⋊C8—113no—
179C2×#103—113no—
180C2×#102—113no—
181C2×C4×C8—113no—
182C22×C11#55012yes—
183C22×C11C22×SD1612yes—
184C22×C11#57712yes—
185C22×C11C23×D411yescharacteristic
186C2×D11—46no—
187C2×D11—46no—
188C2×D11—46no—
189C2×D11—812no—
190C4×C11—26no—
191C4×C11—46no—
192C4×C11—42no—
193C4×C11#55012yes—
194C4×C11C22×SD16112yes—
195C4×C11C22×#4111yescharacteristic
196C4×C11C2×H(5,𝔽2)11yescharacteristic
197Dic11—42no—
198C2×#41—228no—
199C2×#41—448no—
200C22×Q8C22⋊D1111yescharacteristic
201C22×Q8C22×D1113yes—
202C22×D4—113no—
203C22×D4—223no—
204C22×D4—223no—
205C23×C4—223no—
206C2×SD16—1112no—
207C2×SD16—1124no—
208C2×SD16—2212no—
209C2×SD16—4412no—
210C22×C8—111no—
211C22×C8—113no—
212C4⋊Q8—26no—
213C4⋊Q8C22×D11112yes—
214#127—1112no—
215#127—226no—
216#125—224no—
217#121—2224no—
218C4×Q8—28no—
219C4×Q8—26no—
220C4×Q8C22⋊D1114yes—
221C4×Q8C22×D11112yes—
222C4×Q8C22×D1114yes—
223C4×D4—1112no—
224C4×D4—226no—
225C2×C4⋊C4—23no—
226C2×C4⋊C4—23no—
227C2×C4⋊C4—23no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4C22⋊D1113yes—
230C2×C4⋊C4C22×D1111yescharacteristic
231C2×C22⋊C4—223no—
232C2×C42—23no—
233C2×C42C22×D1113yes—
234#106—114no—
235C4⋊C8—1112no—
236#103—1112no—
237#102—1112no—
238C4×C8—1112no—
239C2×C11#339214yescomplemented
240C2×C11C2×#55011yescharacteristic
241C2×C11C23×SD1611yescharacteristic
242C2×C11C2×#57711yescharacteristic
243D11—86no—
244C24—223no—
245#41—4432no—
246C2×Q8—23no—
247C2×Q8—26no—
248C2×Q8—26no—
249C2×Q8#432518yescomplemented
250C2×Q8C2×C22⋊D1114yes—
251C2×Q8C23×D1116yes—
252C2×D4—116no—
253C2×D4—226no—
254C2×D4—226no—
255C2×D4—223no—
256C2×D4—2212no—
257C2×D4—2212no—
258C2×D4—4412no—
259C2×D4—886no—
260C22×C4—21no—
261C22×C4—23no—
262C22×C4—221no—
263C22×C4—2212no—
264C22×C4—4412no—
265C22×C4C2×C22⋊D1113yes—
266C22×C4C2×C22⋊D1113yes—
267C22×C4C23×D1111yescharacteristic
268SD16—2224no—
269SD16—4424no—
270C2×C8—114no—
271C2×C8—112no—
272C2×C8—116no—
273C2×C8—226no—
274C4⋊C4—212no—
275C4⋊C4—212no—
276C4⋊C4—212no—
277C4⋊C4—21no—
278C4⋊C4—112no—
279C4⋊C4—221no—
280C4⋊C4C2×C22⋊D11112yes—
281C4⋊C4C23×D1112yes—
282C22⋊C4—2212no—
283C42—212no—
284C42C2×C22⋊D1116yes—
285C42C23×D1116yes—
286C11C2×#339211yescharacteristic, complemented, Sylow
287C23—226no—
288C23—446no—
289C23—446no—
290C23—446no—
291C23C22×C22⋊D1111yescharacteristic
292Q8—26no—
293Q8—26no—
294Q8—46no—
295Q8C2×#4325116yescomplemented
296D4—226no—
297D4—226no—
298D4—4424no—
299D4—446no—
300D4—8812no—
301C2×C4—26no—
302C2×C4—22no—
303C2×C4—26no—
304C2×C4—46no—
305C2×C4—42no—
306C2×C4—222no—
307C2×C4—442no—
308C2×C4—4424no—
309C2×C4C2×#4325112yes—
310C2×C4#41×D1112yes—
311C2×C4#6704212yes—
312C2×C4C22×C22⋊D1116yes—
313C2×C4C22×C22⋊D1116yes—
314C2×C4C22×C22⋊D1111yescharacteristic
315C2×C4C24×D1111yescharacteristic
316C8—114no—
317C8—226no—
318C22—446no—
319C22—446no—
320C22—446no—
321C22—8812no—
322C22C22×#432512yes—
323C22#1062336512yes—
324C22#1062336812yes—
325C22C23×C22⋊D1111yescharacteristic
326C4—26no—
327C4—42no—
328C4—46no—
329C4—442no—
330C4C22×#4325112yes—
331C4#1062336512yes—
332C4C2×#41×D1111yescharacteristic
333C4C2×#6704211yescharacteristic
334C2—886no—
335C2#1308159314yesdirect product factor
336C2C2×#1062336511yescharacteristic
337C2C23×#432511yescharacteristic
338C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
hypercenterC2×#557D11
hypocenterC11C2×#3392
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081593C2direct (N × H)
3. C2×#10622698C2semidirect
4. C2×#10622640C2semidirect
5. C2×#10622696C2semidirect
6. C2×Q8×C11⋊C8C2semidirect
7. C2×C4×#4325C2semidirect
8. C2×C11×#557C2semidirect
11. C11×#557C22semidirect
25. #10622698C22semidirect
26. #10622696C22semidirect
27. #10622640C22semidirect
28. C4×#4325C22semidirect
29. Q8×C11⋊C8C22semidirect
80. C2×Q8×C11SD16semidirect
115. C2×C11⋊C8#41semidirect
118. C2×#557D11semidirect
134. Q8×C11C2×SD16semidirect
156. C11⋊C8C2×#41semidirect
161. #557C2×D11semidirect
239. C2×C11#3392semidirect
249. C2×Q8#4325semidirect
286. C11C2×#3392semidirect
295. Q8C2×#4325semidirect
335. C2#13081593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231082
#130815932
C2×#106226982
C2×#106226402
C2×#106226962
C2×Q8×C11⋊C82
C2×C4×#43252
C2×C11×#5572
C2×#339211