Finite Group Databasebeta

← C2×#13068163 #14736330

Subgroups — C2×#13068163 #14736330

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622294C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic
3C2×#10622632C211yesmaximal, characteristic
4#13068163C218yesmaximal, direct product factor
5C2×#10622096C211yesmaximal, characteristic, complemented
6C2×#10622120C211yesmaximal, characteristic, complemented
7C2×#10622124C211yesmaximal, characteristic, complemented
8C2×C11×#436C211yesmaximal, characteristic
9C22×C11×M16—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4324—21no—
12C2×#66922C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#436—22no—
15C11×#436C2214yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C22⋊C8—21no—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66896—21no—
20C2×#66880—21no—
21C2×#66880—21no—
22#10622632—22no—
23#10622632C2214yes—
24#10622620—22no—
25#10622620C2214yes—
26C2×#66874—21no—
27C2×#66871—21no—
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622294—22no—
31#10622294C2214yescomplemented
32#10622124C2214yescomplemented
33#10622120C2214yescomplemented
34#10622096C2214yescomplemented
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C22×Dic22—21no—
38C22×Dic22—21no—
39C2×C11×M16—24no—
40C2×C11×M16—44no—
41C22×C8×C11—21no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11D411yescharacteristic
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11D412yes—
47C4×D4×C11C2312yes—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4324—24no—
52C2×#4324—44no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65#66922C2312yes—
66#66922C2312yes—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×C22⋊C8—24no—
70C4×C8×C11D412yes—
71C4×C8×C11C2312yes—
72#66896—24no—
73#66880—24no—
74#66880—24no—
75#66874—24no—
76#66871—24no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)C2312yes—
80C4⋊(C11⋊C8)C2312yes—
81C2×#1699—111nomaximal, Sylow
82C24×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11C2×D412yes—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—41no—
96C22×Dic11—41no—
97C2×Dic22—22no—
98C2×Dic22—22no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×Dic22—42no—
102C2×Dic22—42no—
103C2×Dic22—42no—
104C2×Dic22—42no—
105C11×M16—48no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—42no—
110C2×C8×C11C2×D412yes—
111C2×C8×C11C2×D412yes—
112C11×C4⋊C4—21no—
113C11×C4⋊C4C2×D412yes—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—22no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4324—48no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—42no—
133C2×#487—111no—
134C2×#474—111no—
135C2×#461—111no—
136C2×#436D1111yescharacteristic
137#1699—118no—
138C2×#335—111no—
139C2×#332—111no—
140C2×#332—111no—
141C23×C11—22no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11#12111yescharacteristic
146D4×C11—22no—
147D4×C11—22no—
148D4×C11—42no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#13512yes—
159C2×C4×C11AGL(1,ℤ/8)12yes—
160C2×C4×C11AGL(1,ℤ/8)12yes—
161C2×C4×C11#13712yes—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—82no—
168C2×Dic11—82no—
169Dic22—42no—
170Dic22—42no—
171Dic22—42no—
172Dic22—42no—
173Dic22—82no—
174Dic22—82no—
175C8×C11—22no—
176C8×C11—22no—
177C8×C11—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C22×SD16—221no—
181C22×M16—21no—
182C2×C4⋊Q8—111no—
183C2×C4⋊Q8—111no—
184C2×C4×D4C2×D1111yescharacteristic
185#487—114no—
186#487—222no—
187#474—114no—
188#474—222no—
189#461—114no—
190#461—222no—
191#436—22no—
192#436C2×D1114yes—
193C2×#107—221no—
194C2×C4⋊C8—111no—
195C2×C4⋊C8—111no—
196C2×C4⋊C8C2×D1111yescharacteristic
197C2×#103—221no—
198C2×#103—221no—
199C2×#103—221no—
200C2×#102—221no—
201C2×C22⋊C8—21no—
202C2×C4×C8C2×D1111yescharacteristic
203#335—114no—
204#332—114no—
205#332—114no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—84no—
210C22×C11#46312yes—
211C22×C11#46812yes—
212C22×C11#47312yes—
213C22×C11C2×#12111yescharacteristic
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—42no—
217C4×C11#46312yes—
218C4×C11#46812yes—
219C4×C11C2×#13511yescharacteristic
220C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
222C4×C11C2×#13711yescharacteristic
223Dic11—82no—
224Dic11—82no—
225C22×Q8—221no—
226C22×Q8—221no—
227C22×D4D4411yescharacteristic
228C23×C4—21no—
229C2×SD16—224no—
230C2×SD16—444no—
231C2×M16—24no—
232C2×M16—44no—
233C22×C8—21no—
234C22×C8—221no—
235C22×C8—221no—
236C22×C8C22⋊D1111yescharacteristic
237C22×C8C22⋊D1111yescharacteristic
238C4⋊Q8—112no—
239C4⋊Q8—112no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242C4⋊Q8—221no—
243C4⋊Q8—221no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4D4412yes—
249C4×D4C22×D1112yes—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4D4411yescharacteristic
255C2×C22⋊C4—21no—
256C2×C42C22×D1111yescharacteristic
257#107—224no—
258C4⋊C8—21no—
259C4⋊C8—112no—
260C4⋊C8—112no—
261C4⋊C8—221no—
262C4⋊C8—221no—
263C4⋊C8C22×D1112yes—
264#103—224no—
265#103—224no—
266#103—224no—
267#102—224no—
268C22⋊C8—24no—
269C4×C8C22⋊D1112yes—
270C4×C8C22×D1112yes—
271C2×C11—82no—
272C2×C11#169914yescomplemented
273C2×C11C2×#46311yescharacteristic
274C2×C11C2×#46811yescharacteristic
275C2×C11C2×#47311yescharacteristic
276C24—21no—
277C2×Q8—222no—
278C2×Q8—222no—
279C2×Q8—441no—
280C2×Q8—441no—
281C2×Q8—442no—
282C2×Q8—442no—
283C2×Q8—442no—
284C2×Q8—442no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—21no—
288C2×D4C2×D4412yes—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4C2×D4411yescharacteristic
297C22×C4#433911yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299SD16—448no—
300M16—48no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—42no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—442no—
308C2×C8—442no—
309C2×C8C2×C22⋊D1112yes—
310C2×C8C2×C22⋊D1112yes—
311C4⋊C4—21no—
312C4⋊C4—222no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—222no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C4⋊C4C2×D4412yes—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C42C2×D4411yescharacteristic
324C42#433911yescharacteristic
325C42C2×C22⋊D1111yescharacteristic
326C42C23×D1111yescharacteristic
327C11C2×#169911yescharacteristic, complemented, Sylow
328C23—22no—
329C23—42no—
330C23—42no—
331C23—42no—
332C23#6698311yescharacteristic
333Q8—442no—
334Q8—442no—
335Q8—442no—
336Q8—442no—
337Q8—882no—
338Q8—882no—
339D4—22no—
340D4—22no—
341D4—42no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—882no—
351C2×C4—882no—
352C2×C4#6696112yes—
353C2×C4#6696212yes—
354C2×C4#6698311yescharacteristic
355C2×C4#6698311yescharacteristic
356C2×C4#6698311yescharacteristic
357C2×C4#6698512yes—
358C2×C4#6700312yes—
359C2×C4C22×D4411yescharacteristic
360C2×C4C2×#433911yescharacteristic
361C2×C4C22×C22⋊D1111yescharacteristic
362C8—22no—
363C8—22no—
364C8—42no—
365C8—442no—
366C8—442no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—84no—
371C22#1062262912yes—
372C22#1062274712yes—
373C22#1062275612yes—
374C22C2×#6698311yescharacteristic
375C4—21no—
376C4—21no—
377C4—42no—
378C4—882no—
379C4—882no—
380C4#1062262912yes—
381C4#1062274712yes—
382C4C2×#6696111yescharacteristic
383C4C2×#6696211yescharacteristic
384C4C2×#6698511yescharacteristic
385C4C2×#6700311yescharacteristic
386C2—82no—
387C2#1306816314yesdirect product factor
388C2C2×#1062262911yescharacteristic
389C2C2×#1062274711yescharacteristic
390C2C2×#1062275611yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#436C2
socleC23×C11#121
prime radicalC22×D4×C11D4
hypercenterC2×#436D11
hypocenterC11C2×#1699
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#10622294C2semidirect
4. #13068163C2direct (N × H)
5. C2×#10622096C2semidirect
6. C2×#10622120C2semidirect
7. C2×#10622124C2semidirect
31. #10622294C22semidirect
32. #10622124C22semidirect
33. #10622120C22semidirect
34. #10622096C22semidirect
272. C2×C11#1699semidirect
327. C11C2×#1699semidirect
387. C2#13068163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106222942
C2×#106226202
C2×#106226322
#130681632
C2×#106220962
C2×#106221202
C2×#106221242
C2×C11×#4362
C2×#169911