Finite Group Databasebeta

← C2×#13068117 #14736296

Subgroups — C2×#13068117 #14736296

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622692C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic
3C2×#10622625C211yesmaximal, characteristic
4#13068117C218yesmaximal, direct product factor
5C2×#10622117C211yesmaximal, characteristic, complemented
6C2×#10622184C211yesmaximal, characteristic, complemented
7C2×#10622120C211yesmaximal, characteristic, complemented
8C2×C11×#476C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4324—21no—
12C22×#4318—21no—
13C2×#66922C2211yescharacteristic
14C11×#476—22no—
15C11×#476C2214yes—
16C2×C11×#106—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102—21no—
19C2×C22⋊(C11⋊C8)—21no—
20#10622692—22no—
21#10622692C2214yescomplemented
22#10622632—22no—
23#10622632C2214yes—
24#10622625—22no—
25#10622625C2214yes—
26C2×#66874—21no—
27C2×#66872—21no—
28C2×#66872—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622184C2214yescomplemented
33#10622120C2214yescomplemented
34#10622117C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C22×Dic22—21no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8C2312yes—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11D412yes—
47C4×D4×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4324—24no—
54C2×#4324—44no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×#4318—24no—
58C2×#4318—44no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922C2312yes—
67C11×#106—24no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×#102—24no—
71C22⋊(C11⋊C8)—24no—
72#66874—24no—
73#66872—24no—
74#66872—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)C2312yes—
78C4⋊(C11⋊C8)C2312yes—
79C4×C11⋊C8D412yes—
80C4×C11⋊C8C2312yes—
81C2×#1691—111nomaximal, Sylow
82C24×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—41no—
85C2×Q8×C11—82no—
86C2×D4×C11—21no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11C2×D412yes—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—41no—
100C2×Dic22—22no—
101C2×Dic22—41no—
102C2×Dic22—42no—
103C2×Dic22—42no—
104C2×C8×C11—22no—
105C2×C8×C11—42no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4C2×D412yes—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—22no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118#4324—48no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123#4318—48no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8SD1614yescomplemented
130C2×C11⋊C8C2×D412yes—
131C2×C11⋊C8C2×D412yes—
132C2×#498—111no—
133C2×#476D1111yescharacteristic
134C2×#461—111no—
135C2×#436—111no—
136#1691—118no—
137C2×#335—111no—
138C2×#333—111no—
139C2×#332—111no—
140C23×C11—22no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11#12111yescharacteristic
145Q8×C11—82no—
146Q8×C11—82no—
147D4×C11—22no—
148D4×C11—22no—
149D4×C11—42no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—44no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11C2×SD1612yes—
162C2×C4×C11AGL(1,ℤ/8)12yes—
163C2×C4×C11#13712yes—
164C2×C4×C11#13712yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×Dic11—42no—
169C2×Dic11—82no—
170Dic22—42no—
171Dic22—42no—
172Dic22—82no—
173C8×C11—42no—
174C11⋊C8—22no—
175C11⋊C8—42no—
176C11⋊C8—42no—
177C11⋊C8C2×SD1614yescomplemented
178C22×SD16—221no—
179C22×M16—221no—
180C2×C4⋊Q8—111no—
181C2×C4⋊Q8C2×D1111yescharacteristic
182C2×C4×D4C2×D1111yescharacteristic
183#498—114no—
184#498—222no—
185#476—22no—
186#476C2×D1114yes—
187#461—114no—
188#461—222no—
189#436—114no—
190#436—222no—
191C2×#106—21no—
192C2×#106—221no—
193C2×#106—221no—
194C2×C4⋊C8—111no—
195C2×C4⋊C8—111no—
196C2×C4⋊C8C2×D1111yescharacteristic
197C2×#103—221no—
198C2×#102—21no—
199C2×C22⋊C8—221no—
200C2×C4×C8—111no—
201#335—114no—
202#333—114no—
203#332—114no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11—84no—
208C22×C11#46112yes—
209C22×C11#46812yes—
210C22×C11#47112yes—
211C22×C11C2×#12111yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—82no—
216C4×C11#46112yes—
217C4×C11#46812yes—
218C4×C11C22×SD1611yescharacteristic
219C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
220C4×C11C2×#13711yescharacteristic
221C4×C11C2×#13711yescharacteristic
222Dic11—82no—
223C22×Q8—21no—
224C22×Q8—221no—
225C22×D4C22⋊D1111yescharacteristic
226C23×C4—21no—
227C2×SD16—224no—
228C2×SD16—444no—
229C2×M16—224no—
230C2×M16—444no—
231C22×C8—21no—
232C22×C8—111no—
233C22×C8—111no—
234C22×C8—221no—
235C22×C8—221no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—112no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242C4⋊Q8—221no—
243C4⋊Q8C22×D1112yes—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4C22⋊D1112yes—
247C4×D4C22×D1112yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C22×D1111yescharacteristic
255#106—24no—
256#106—224no—
257#106—224no—
258C4⋊C8—21no—
259C4⋊C8—112no—
260C4⋊C8—112no—
261C4⋊C8—221no—
262C4⋊C8—221no—
263C4⋊C8C22×D1112yes—
264#103—224no—
265#102—24no—
266C22⋊C8—224no—
267C4×C8—112no—
268C4×C8—112no—
269C2×C11—82no—
270C2×C11#169114yescomplemented
271C2×C11C2×#46111yescharacteristic
272C2×C11C2×#46811yescharacteristic
273C2×C11C2×#47111yescharacteristic
274C24—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—82no—
278C2×Q8—222no—
279C2×Q8—441no—
280C2×Q8—442no—
281C2×Q8—442no—
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4C2×C22⋊D1112yes—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—441no—
293C22×C4D4×D1111yescharacteristic
294C22×C4#434111yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296SD16—448no—
297M16—448no—
298C2×C8—22no—
299C2×C8—42no—
300C2×C8—114no—
301C2×C8—112no—
302C2×C8—112no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—442no—
307C2×C8—442no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4C2×C22⋊D1112yes—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C42D4×D1111yescharacteristic
321C42#434111yescharacteristic
322C42C2×C22⋊D1111yescharacteristic
323C42C23×D1111yescharacteristic
324C11C2×#169111yescharacteristic, complemented, Sylow
325C23—22no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23#6699211yescharacteristic
330Q8—82no—
331Q8—82no—
332Q8—442no—
333Q8—442no—
334Q8—882no—
335D4—22no—
336D4—22no—
337D4—42no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—44no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—442no—
347C2×C4—882no—
348C2×C4SD16×D1112yes—
349C2×C4#6696812yes—
350C2×C4#6699211yescharacteristic
351C2×C4#6699211yescharacteristic
352C2×C4#6699211yescharacteristic
353C2×C4#6699512yes—
354C2×C4#6700212yes—
355C2×C4C2×D4×D1111yescharacteristic
356C2×C4C2×#434111yescharacteristic
357C2×C4C22×C22⋊D1111yescharacteristic
358C8—42no—
359C8—114no—
360C8—222no—
361C8—442no—
362C8—442no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—84no—
367C22#1062266212yes—
368C22#1062277512yes—
369C22#1062281312yes—
370C22C2×#6699211yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—82no—
375C4—882no—
376C4#1062266212yes—
377C4#1062277512yes—
378C4C2×SD16×D1111yescharacteristic
379C4C2×#6696811yescharacteristic
380C4C2×#6699511yescharacteristic
381C4C2×#6700211yescharacteristic
382C2—82no—
383C2#1306811714yesdirect product factor
384C2C2×#1062277511yescharacteristic
385C2C2×#1062266211yescharacteristic
386C2C2×#1062281311yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#476C2
socleC23×C11#121
prime radicalC22×D4×C11D4
hypercenterC2×#476D11
hypocenterC11C2×#1691
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10622692C2semidirect
4. #13068117C2direct (N × H)
5. C2×#10622117C2semidirect
6. C2×#10622184C2semidirect
7. C2×#10622120C2semidirect
21. #10622692C22semidirect
32. #10622184C22semidirect
33. #10622120C22semidirect
34. #10622117C22semidirect
129. C2×C11⋊C8SD16semidirect
177. C11⋊C8C2×SD16semidirect
270. C2×C11#1691semidirect
324. C11C2×#1691semidirect
383. C2#13068117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226922
C2×#106226322
C2×#106226252
#130681172
C2×#106221172
C2×#106221842
C2×#106221202
C2×C11×#4762
C2×#169111