Finite Group Databasebeta

← C2×#13068147 #14736320

Subgroups — C2×#13068147 #14736320

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068147C218yesmaximal, direct product factor
5C2×#10622117C211yesmaximal, characteristic, complemented
6C2×#10622119C211yesmaximal, characteristic, complemented
7C2×#10622182C211yesmaximal, characteristic, complemented
8C2×C11×#459C211yesmaximal, characteristic
9C22×C11×D8—21no—
10C2×C11×#127C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C22×#4318—21no—
13C2×#66922C2211yescharacteristic
14C11×#459—22no—
15C11×#459C2214yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102—21no—
18C2×#66896—21no—
19C2×#66896—21no—
20C2×#66896—21no—
21C2×C22⋊(C11⋊C8)—21no—
22#10622683—22no—
23#10622683C2214yescomplemented
24#10622625—22no—
25#10622625C2214yescomplemented
26#10622621—22no—
27#10622621C2214yescomplemented
28C2×#66872—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622182C2214yescomplemented
33#10622119C2214yescomplemented
34#10622117C2214yescomplemented
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C22×Dic22—21no—
41C2×C11×D8—24no—
42C2×C11×D8—44no—
43C22×C8×C11—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127C2312yes—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11D412yes—
51C4×D4×C11C2312yes—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C22⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
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×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×#102—24no—
70#66896—24no—
71#66896—24no—
72#66896—24no—
73C22⋊(C11⋊C8)—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×#1697—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C2×D4×C11—82no—
98C2×D4×C11C2×D412yes—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×Dic11—41no—
108C2×Dic22—22no—
109C2×Dic22—41no—
110C2×Dic22—82no—
111C11×D8—48no—
112C2×C8×C11—22no—
113C2×C8×C11—42no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4C2×D412yes—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—22no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11C2411yescharacteristic
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126#4318—48no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—42no—
133C2×C11⋊C8C2×D412yes—
134C2×C11⋊C8C2×D412yes—
135C2×#486—111no—
136C2×#476—111no—
137C2×#459D1111yescharacteristic
138C2×#436—111no—
139#1697—118no—
140C2×#335—111no—
141C2×#333—111no—
142C2×#331—111no—
143C23×C11—22no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—82no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11#12111yescharacteristic
152D4×C11—22no—
153D4×C11—22no—
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—82no—
162D4×C11—82no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—44no—
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#13512yes—
173C2×C4×C11AGL(1,ℤ/8)12yes—
174C2×C4×C11AGL(1,ℤ/8)12yes—
175C2×C4×C11#13712yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×Dic11—42no—
180C2×Dic11—82no—
181Dic22—82no—
182Dic22—82no—
183C8×C11—42no—
184C11⋊C8—22no—
185C11⋊C8—22no—
186C11⋊C8—42no—
187C11⋊C8—42no—
188C22×D8—21no—
189C22×M16—221no—
190C2×C4⋊Q8—111no—
191C2×#127C2×D1111yescharacteristic
192C2×C4×D4C2×D1111yescharacteristic
193#486—114no—
194#486—222no—
195#476—114no—
196#476—222no—
197#459—22no—
198#459C2×D1114yes—
199#436—114no—
200#436—222no—
201C2×#106—221no—
202C2×C4⋊C8—111no—
203C2×C4⋊C8—111no—
204C2×C4⋊C8C2×D1111yescharacteristic
205C2×#102—21no—
206C2×#102—221no—
207C2×#102—221no—
208C2×#102—221no—
209C2×C22⋊C8—221no—
210C2×C4×C8—111no—
211#335—114no—
212#333—114no—
213#331—114no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—84no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—164no—
222C22×C11#46312yes—
223C22×C11#46812yes—
224C22×C11#47212yes—
225C22×C11C2×#12111yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11#46312yes—
230C4×C11#46812yes—
231C4×C11C2×#13511yescharacteristic
232C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C11C2×#13711yescharacteristic
235Dic11—82no—
236C22×Q8—221no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4C22⋊D1111yescharacteristic
241C23×C4—21no—
242C2×D8—24no—
243C2×D8—44no—
244C2×M16—224no—
245C2×M16—444no—
246C22×C8—21no—
247C22×C8—111no—
248C22×C8—111no—
249C22×C8—221no—
250C22×C8—221no—
251C4⋊Q8—112no—
252C4⋊Q8—221no—
253C4⋊Q8—221no—
254C4⋊Q8—221no—
255#127—21no—
256#127—21no—
257#127—21no—
258#127C22×D1112yes—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4C22⋊D1112yes—
262C4×D4C22×D1112yes—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4C22⋊D1111yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C22×D1111yescharacteristic
268#106—224no—
269C4⋊C8—21no—
270C4⋊C8—112no—
271C4⋊C8—112no—
272C4⋊C8—221no—
273C4⋊C8—221no—
274C4⋊C8C22×D1112yes—
275#102—24no—
276#102—224no—
277#102—224no—
278#102—224no—
279C22⋊C8—224no—
280C4×C8—112no—
281C4×C8—112no—
282C2×C11—82no—
283C2×C11—162no—
284C2×C11#169714yescomplemented
285C2×C11C2×#46311yescharacteristic
286C2×C11C2×#46811yescharacteristic
287C2×C11C2×#47211yescharacteristic
288C24—21no—
289C24—41no—
290C2×Q8—222no—
291C2×Q8—441no—
292C2×Q8—882no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—42no—
306C2×D4—82no—
307C2×D4C2×C22⋊D1112yes—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—441no—
314C22×C4D4×D1111yescharacteristic
315C22×C4#434111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317D8—48no—
318M16—448no—
319C2×C8—22no—
320C2×C8—42no—
321C2×C8—112no—
322C2×C8—112no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—442no—
328C2×C8—442no—
329C4⋊C4—21no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C4⋊C4C2×C22⋊D1112yes—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C42D4×D1111yescharacteristic
338C42#434111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C42C23×D1111yescharacteristic
341C11C2×#169711yescharacteristic, complemented, Sylow
342C23—22no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—82no—
348C23—82no—
349C23—82no—
350C23#6699211yescharacteristic
351Q8—882no—
352Q8—882no—
353D4—22no—
354D4—22no—
355D4—42no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—42no—
360D4—82no—
361D4—82no—
362D4—82no—
363D4—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—442no—
371C2×C4—882no—
372C2×C4#6696412yes—
373C2×C4#6696512yes—
374C2×C4#6698512yes—
375C2×C4#6699211yescharacteristic
376C2×C4#6699211yescharacteristic
377C2×C4#6699211yescharacteristic
378C2×C4#6700412yes—
379C2×C4C2×D4×D1111yescharacteristic
380C2×C4C2×#434111yescharacteristic
381C2×C4C22×C22⋊D1111yescharacteristic
382C8—42no—
383C8—222no—
384C8—222no—
385C8—442no—
386C8—442no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—84no—
391C22—82no—
392C22—82no—
393C22—82no—
394C22—164no—
395C22#1062265512yes—
396C22#1062276612yes—
397C22#1062281212yes—
398C22C2×#6699211yescharacteristic
399C4—21no—
400C4—21no—
401C4—42no—
402C4—882no—
403C4#1062265512yes—
404C4#1062276612yes—
405C4C2×#6696411yescharacteristic
406C4C2×#6696511yescharacteristic
407C4C2×#6698511yescharacteristic
408C4C2×#6700411yescharacteristic
409C2—82no—
410C2—162no—
411C2#1306814714yesdirect product factor
412C2C2×#1062276611yescharacteristic
413C2C2×#1062265511yescharacteristic
414C2C2×#1062281211yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11#121
hypercenterC2×#459D11
hypocenterC11C2×#1697
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622683C2semidirect
2. C2×#10622621C2semidirect
3. C2×#10622625C2semidirect
4. #13068147C2direct (N × H)
5. C2×#10622117C2semidirect
6. C2×#10622119C2semidirect
7. C2×#10622182C2semidirect
23. #10622683C22semidirect
25. #10622625C22semidirect
27. #10622621C22semidirect
32. #10622182C22semidirect
33. #10622119C22semidirect
34. #10622117C22semidirect
284. C2×C11#1697semidirect
341. C11C2×#1697semidirect
411. C2#13068147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226832
C2×#106226212
C2×#106226252
#130681472
C2×#106221172
C2×#106221192
C2×#106221822
C2×C11×#4592
C2×#169711