Finite Group Databasebeta

← C2×#13068286 #14741558

Subgroups — C2×#13068286 #14741558

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622705C211yesmaximal, characteristic, complemented
3C2×#10622698C211yesmaximal, characteristic
4C2×#10622701C211yesmaximal, characteristic
5C2×#10622307C211yesmaximal, characteristic
6#13068286C218yesmaximal, direct product factor
7C2×#10622092C211yesmaximal, characteristic, complemented
8C2×C11×#500C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C22×#4326—22no—
12C22×#4325—22no—
13C2×#66927C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#500—22no—
16C11×#500C2214yescomplemented
17C2×C11×#107—22no—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66885—22no—
20#10622705—22no—
21#10622705C2214yescomplemented
22#10622701—22no—
23#10622701C2214yes—
24#10622698—22no—
25#10622698C2214yes—
26#10622691—22no—
27#10622691C2214yescomplemented
28C2×#66873—22no—
29C2×#66871—22no—
30C2×C4×C11⋊C8C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622307—22no—
33#10622307C2214yes—
34#10622092C2214yescomplemented
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×Dic22—21no—
41C22×C8×C11D412yes—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8C2312yes—
49C11×C4⋊Q8C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4326—28no—
56C2×#4326—48no—
57C2×#4325—28no—
58C2×#4325—48no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C22×C11⋊C8D412yes—
62C22×C11⋊C8D412yes—
63#66927—21no—
64#66927—21no—
65#66927—21no—
66#66927C2312yes—
67#66922—21no—
68#66922—21no—
69#66922—21no—
70#66922C2312yes—
71C11×#107—28no—
72C4×C8×C11D412yes—
73C4×C8×C11C2312yes—
74#66885—28no—
75#66873—28no—
76#66871—28no—
77C4×C11⋊C8D412yes—
78C4×C11⋊C8D412yes—
79C4×C11⋊C8C2312yes—
80C4×C11⋊C8C2312yes—
81C2×#1722—111nomaximal, Sylow
82C23×D11—41no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—44no—
88C2×Q8×C11—44no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—41no—
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—44no—
102C2×D44—44no—
103C2×D44—44no—
104C2×Dic22—22no—
105C2×Dic22—41no—
106C2×Dic22—44no—
107C2×C8×C11—24no—
108C2×C8×C11C2×D414yes—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2411yescharacteristic
121#4326—416no—
122#4325—416no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C2×C11⋊C8—24no—
128C2×C11⋊C8D818yes—
129C2×C11⋊C8C2×D414yes—
130C2×C11⋊C8C2×D414yes—
131C2×#500—111no—
132C2×#500D1111yescharacteristic, complemented
133C2×#494—111no—
134C2×#492—111no—
135C2×#486—111no—
136C2×#486—111no—
137#1722—118no—
138C2×#322—111no—
139C23×C11#12711yescharacteristic
140C22×D11—42no—
141C22×D11—82no—
142C22×D11—82no—
143C22×D11—82no—
144Q8×C11—44no—
145Q8×C11—44no—
146Q8×C11—82no—
147Q8×C11—82no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×C4×C11C2×D814yes—
156C2×C4×C11#13714yes—
157C2×C4×C11#13714yes—
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×Dic11—42no—
162C2×Dic11—82no—
163D44—44no—
164D44—44no—
165D44—44no—
166D44—82no—
167D44—82no—
168D44—82no—
169Dic22—44no—
170Dic22—82no—
171C8×C11—24no—
172C11⋊C8—24no—
173C11⋊C8C2×D818yes—
174C22×Q16—222no—
175C22×SD16—222no—
176C2×C4⋊Q8—111no—
177C2×C4⋊Q8C2×D1111yescharacteristic
178C2×C4⋊Q8C2×D1111yescharacteristic
179C2×#127—111no—
180#500—22no—
181#500—114no—
182#500—222no—
183#500C2×D1114yescomplemented
184#494—114no—
185#494—222no—
186#492—114no—
187#492—222no—
188#486—114no—
189#486—114no—
190#486—222no—
191#486—222no—
192C2×#107—22no—
193C2×#107—222no—
194C2×#102—222no—
195C2×#102—222no—
196C2×C4×C8—111no—
197C2×C4×C8—111no—
198C2×C4×C8C2×D1111yescharacteristic
199#322—114no—
200C22×C11#49312yes—
201C22×C11#49712yes—
202C22×C11#49712yes—
203C22×C11C2×#12711yescharacteristic
204C2×D11—82no—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—164no—
208C4×C11—82no—
209C4×C11—82no—
210C4×C11#49312yes—
211C4×C11#49712yes—
212C4×C11#49712yes—
213C4×C11C22×D812yes—
214C4×C11C2×#13712yes—
215C4×C11C2×#13712yes—
216Dic11—82no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—221no—
220C22×D4—221no—
221C22×D4—221no—
222C22×D4—221no—
223C2×Q16—228no—
224C2×Q16—448no—
225C2×SD16—228no—
226C2×SD16—448no—
227C22×C8—112no—
228C22×C8—112no—
229C22×C8C22⋊D1112yes—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—112no—
237C4⋊Q8—221no—
238C4⋊Q8—221no—
239C4⋊Q8—221no—
240C4⋊Q8C22×D1112yes—
241C4⋊Q8C22×D1112yes—
242#127—112no—
243#127—221no—
244#127—221no—
245#127—221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C42C22×D1111yescharacteristic
253#107—28no—
254#107—228no—
255#102—228no—
256#102—228no—
257C4×C8—112no—
258C4×C8—112no—
259C4×C8—112no—
260C4×C8—112no—
261C4×C8C22⋊D1112yes—
262C4×C8C22×D1112yes—
263C2×C11#172214yescomplemented
264C2×C11C2×#49311yescharacteristic
265C2×C11C2×#49711yescharacteristic
266C2×C11C2×#49711yescharacteristic
267D11—162no—
268C24—441no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—44no—
274C2×Q8—44no—
275C2×Q8—222no—
276C2×Q8—441no—
277C2×Q8—444no—
278C2×D4—222no—
279C2×D4—222no—
280C2×D4—222no—
281C2×D4—444no—
282C2×D4—444no—
283C2×D4—441no—
284C2×D4—441no—
285C2×D4—441no—
286C2×D4—444no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—441no—
290C22×C4D4×D1111yescharacteristic
291C22×C4D4×D1111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293Q16—4416no—
294SD16—4416no—
295C2×C8—24no—
296C2×C8—118no—
297C2×C8—114no—
298C2×C8—114no—
299C2×C8—224no—
300C2×C8C2×C22⋊D1114yes—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—222no—
310C4⋊C4—222no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C42D4×D1111yescharacteristic
314C42D4×D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C42C23×D1111yescharacteristic
317C11C2×#172211yescharacteristic, complemented, Sylow
318C23—442no—
319C23—882no—
320C23—882no—
321C23—882no—
322C23#6699311yescharacteristic
323Q8—44no—
324Q8—44no—
325Q8—82no—
326Q8—82no—
327Q8—444no—
328Q8—882no—
329D4—444no—
330D4—444no—
331D4—444no—
332D4—882no—
333D4—882no—
334D4—882no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—442no—
340C2×C4—882no—
341C2×C4D8×D1114yes—
342C2×C4#6697114yes—
343C2×C4#6699311yescharacteristic
344C2×C4#6699311yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6699514yes—
347C2×C4C2×D4×D1111yescharacteristic
348C2×C4C2×D4×D1111yescharacteristic
349C2×C4C22×C22⋊D1111yescharacteristic
350C8—24no—
351C8—118no—
352C8—224no—
353C22—882no—
354C22—882no—
355C22—882no—
356C22—1764no—
357C22#1062269912yes—
358C22#1062276412yes—
359C22#1062280312yes—
360C22C2×#6699311yescharacteristic
361C4—82no—
362C4—82no—
363C4—882no—
364C4#1062269912yes—
365C4#1062276412yes—
366C4#1062280312yes—
367C4C2×D8×D1112yes—
368C4C2×#6697112yes—
369C4C2×#6699512yes—
370C2—1762no—
371C2#1306828614yesdirect product factor
372C2C2×#1062276411yescharacteristic
373C2C2×#1062269911yescharacteristic
374C2C2×#1062280311yescharacteristic
subgroupG/H
centerC23#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#500C2
socleC23×C11#127
prime radicalC2×#66927C22
hypercenterC2×#500D11
hypocenterC11C2×#1722
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
2. C2×#10622705C2semidirect
6. #13068286C2direct (N × H)
7. C2×#10622092C2semidirect
8. C2×C11×#500C2semidirect
16. C11×#500C22semidirect
21. #10622705C22semidirect
27. #10622691C22semidirect
34. #10622092C22semidirect
132. C2×#500D11semidirect
183. #500C2×D11semidirect
263. C2×C11#1722semidirect
317. C11C2×#1722semidirect
371. C2#13068286direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226912
C2×#106227052
C2×#106226982
C2×#106227012
C2×#106223072
#130682862
C2×#106220922
C2×C11×#5002
C2×#172211