Finite Group Databasebeta

← C2×#13070682 #14908142

Subgroups — C2×#13070682 #14908142

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic, complemented
2C2×#10622760C211yesmaximal, characteristic
3C2×#10622313C211yesmaximal, characteristic, complemented
4#13070682C218yesmaximal, direct product factor
5C2×#10622101C211yesmaximal, characteristic, complemented
6C2×#10622203C211yesmaximal, characteristic, complemented
7C2×#10622201C211yesmaximal, characteristic, complemented
8C2×C11×#495C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic
10C22×C11×SD16—21no—
11C22×C11×D8C2211yescharacteristic
12C2×C11×#124—21no—
13C2×#66957C2211yescharacteristic
14C2×#66954—21no—
15C11×#495—22no—
16C11×#495C2214yescomplemented
17C2×C4×C8×C11C2211yescharacteristic
18C2×#66893—21no—
19#10622792—22no—
20#10622792C2214yescomplemented
21C2×#66892—21no—
22C2×#66891—21no—
23#10622760—22no—
24#10622760C2214yes—
25C2×#66890—21no—
26C2×#66883C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C2×#66876C2211yescharacteristic
29C2×#66869—21no—
30#10622313—22no—
31#10622313C2214yescomplemented
32#10622203C2214yescomplemented
33#10622201C2214yescomplemented
34#10622101C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11—21no—
37C2×#4339—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C2×C11×Q16—21no—
41C2×C11×Q16—21no—
42C2×C11×Q16—21no—
43C2×C11×Q16C2312yes—
44C2×C11×SD16—24no—
45C2×C11×SD16—41no—
46C2×C11×SD16—41no—
47C2×C11×SD16—42no—
48C2×C11×D8—21no—
49C2×C11×D8—21no—
50C2×C11×D8—21no—
51C2×C11×D8—21no—
52C2×C11×D8—21no—
53C2×C11×D8C2312yes—
54C22×C8×C11D411yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×#124—24no—
57C11×#124—42no—
58C2×C11×C22⋊C4—42no—
59C2×C42×C11D411yescharacteristic
60C2×#4318—21no—
61C2×Dic44D411yescharacteristic
62#66957—21no—
63#66957—21no—
64#66957D412yes—
65#66957C2312yes—
66C2×D88D411yescharacteristic
67C2×#4314—21no—
68#66954—24no—
69#66954—42no—
70C2×#4313—41no—
71C2×C8×D11—41no—
72C4×C8×C11D412yes—
73C4×C8×C11C2312yes—
74#66893—24no—
75#66892—24no—
76#66891—24no—
77#66890—24no—
78#66883—21no—
79#66883C2312yes—
80#66876—21no—
81#66876—21no—
82#66876C2312yes—
83#66876C2312yes—
84C2×C11⋊C16—21no—
85C2×C11⋊C16—21no—
86#66869—24no—
87C2×#2212—111nomaximal, Sylow
88C24×C11—41no—
89C2×Q8×C11—22no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×Q8×C11—41no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×D4×C11—22no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—41no—
105#4339—22no—
106#4339—22no—
107#4339—41no—
108#4339—41no—
109C2×D44—21no—
110C2×C4×D11—41no—
111C2×Dic22—21no—
112C11×Q16—22no—
113C11×Q16—22no—
114C11×Q16—41no—
115C11×Q16—41no—
116C11×SD16—44no—
117C11×SD16—44no—
118C11×D8—22no—
119C11×D8—22no—
120C11×D8—41no—
121C11×D8—41no—
122C2×C8×C11D811yescharacteristic
123C2×C8×C11D811yescharacteristic
124C2×C8×C11D812yes—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D412yes—
129C2×C8×C11#4111yescharacteristic
130C2×C8×C11#4111yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C22⋊C4—48no—
133C42×C11—21no—
134C42×C11C2×D412yes—
135#4318—22no—
136#4318—41no—
137C2×C11⋊C8—41no—
138Dic44—21no—
139Dic44C2×D412yes—
140D88—21no—
141D88C2×D412yes—
142#4314—22no—
143#4314—22no—
144#4313—44no—
145C8×D11—44no—
146C11⋊C16—22no—
147C11⋊C16—22no—
148C2×#510—111no—
149C2×#509—111no—
150C2×#495D1111yescharacteristic, complemented
151C2×#443—111no—
152#2212—118no—
153C2×#364—111no—
154C2×#362—111no—
155C2×#361—111no—
156C23×C11—42no—
157C23×C11—84no—
158C23×C11—81no—
159C23×C11—81no—
160C23×C11AGL(1,ℤ/8)11yescharacteristic
161C22×D11—41no—
162Q8×C11—42no—
163Q8×C11—42no—
164Q8×C11—81no—
165Q8×C11—81no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—81no—
169D4×C11—81no—
170C2×C4×C11—22no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C22⋊D11—42no—
182C22⋊D11—42no—
183C2×Dic11—41no—
184D44—22no—
185D44—41no—
186C4×D11—42no—
187C4×D11—42no—
188Dic22—22no—
189Dic22—41no—
190C8×C11#12111yescharacteristic
191C8×C11#12111yescharacteristic
192C8×C11C2×D812yes—
193C8×C11C2×D812yes—
194C8×C11C22×D411yescharacteristic
195C8×C11C2×#4111yescharacteristic
196C11⋊C8—42no—
197C2×#135—111no—
198C22×Q16C2×D1111yescharacteristic
199C22×SD16—21no—
200C22×D8C2×D1111yescharacteristic
201C2×#131—221no—
202C2×#124—21no—
203#510—114no—
204#510—222no—
205#509—114no—
206#509—222no—
207C2×Q32—221no—
208C2×SD32—221no—
209C2×SD32—221no—
210C2×D16—221no—
211C2×M32—111no—
212C2×M32—111no—
213#495—22no—
214#495C2×D1114yescomplemented
215#443—114no—
216#443—222no—
217C2×#108—111no—
218C2×#104—221no—
219C2×C4×C8C2×D1111yescharacteristic
220#364—114no—
221#362—114no—
222#361—114no—
223C22×C11—22no—
224C22×C11—84no—
225C22×C11—82no—
226C22×C11—162no—
227C22×C11—162no—
228C22×C11#45911yescharacteristic
229C22×C11#45911yescharacteristic
230C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
231C2×D11—42no—
232C2×D11—82no—
233C4×C11—42no—
234C4×C11—82no—
235C4×C11#45911yescharacteristic
236C4×C11#45911yescharacteristic
237C4×C11C2×#12111yescharacteristic
238C4×C11C22×D811yescharacteristic
239Dic11—42no—
240C2×#41—221no—
241C22×Q8—21no—
242C22×D4—21no—
243#135—112no—
244#135—112no—
245#135—221no—
246#135—221no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16—111no—
253C2×Q16C22×D1112yes—
254C2×SD16—24no—
255C2×SD16—41no—
256C2×SD16—41no—
257C2×SD16—42no—
258C2×SD16—221no—
259C2×D8—21no—
260C2×D8—21no—
261C2×D8—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—111no—
265C2×D8C22×D1112yes—
266#131—224no—
267#131—442no—
268C2×M16—221no—
269C2×M16—441no—
270C22×C8—441no—
271C22×C8C22⋊D1111yescharacteristic
272C22×C8C22×D1111yescharacteristic
273#124—24no—
274#124—42no—
275C2×C22⋊C4—42no—
276C2×C42C22⋊D1111yescharacteristic
277Q32—224no—
278SD32—224no—
279SD32—224no—
280D16—224no—
281M32—112no—
282M32—112no—
283M32—221no—
284M32—221no—
285C2×C16—221no—
286C2×C16—221no—
287#108—112no—
288#108—221no—
289#104—224no—
290C4×C8C22⋊D1112yes—
291C4×C8C22×D1112yes—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—162no—
295C2×C11#221212yescomplemented
296C2×C11C2×#45911yescharacteristic
297D11—82no—
298C24—41no—
299#41—222no—
300#41—222no—
301#41—441no—
302#41—441no—
303C2×Q8—22no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—221no—
310C2×D4—22no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—221no—
317C2×D4—441no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—441no—
321C22×C4C2×C22⋊D1111yescharacteristic
322Q16—22no—
323Q16—22no—
324Q16—41no—
325Q16—41no—
326Q16—112no—
327Q16—221no—
328SD16—44no—
329SD16—44no—
330SD16—222no—
331SD16—222no—
332D8—22no—
333D8—22no—
334D8—41no—
335D8—41no—
336D8—112no—
337D8—221no—
338M16—222no—
339M16—441no—
340M16—444no—
341C2×C8—441no—
342C2×C8—444no—
343C2×C8#432311yescharacteristic
344C2×C8#432311yescharacteristic
345C2×C8#432312yes—
346C2×C8D4×D1111yescharacteristic
347C2×C8D4×D1111yescharacteristic
348C2×C8#434111yescharacteristic
349C2×C8#434111yescharacteristic
350C2×C8C2×C22⋊D1112yes—
351C2×C8C2×C22⋊D1111yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C22⋊C4—48no—
354C42—21no—
355C42C2×C22⋊D1112yes—
356C16—222no—
357C16—222no—
358C11C2×#221211yescharacteristic, complemented, Sylow
359C23—42no—
360C23—84no—
361C23—81no—
362C23—81no—
363C23—441no—
364C23#6698511yescharacteristic
365Q8—42no—
366Q8—42no—
367Q8—81no—
368Q8—81no—
369Q8—222no—
370Q8—441no—
371D4—42no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—222no—
376D4—442no—
377D4—442no—
378D4—441no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4C2×#432311yescharacteristic
388C2×C4C2×#432311yescharacteristic
389C2×C4#6698511yescharacteristic
390C2×C4#6699111yescharacteristic
391C2×C4#6699111yescharacteristic
392C2×C4C22×C22⋊D1111yescharacteristic
393C8—442no—
394C8C2×#432312yes—
395C8C2×#432312yes—
396C8#6699111yescharacteristic
397C8#6699111yescharacteristic
398C8C2×D4×D1111yescharacteristic
399C8C2×#434111yescharacteristic
400C22—22no—
401C22—84no—
402C22—82no—
403C22—162no—
404C22—162no—
405C22—442no—
406C22—882no—
407C22#1062268511yescharacteristic
408C22#1062268511yescharacteristic
409C22C2×#6698511yescharacteristic
410C4—42no—
411C4—82no—
412C4—442no—
413C4#1062268511yescharacteristic
414C4#1062268511yescharacteristic
415C4C22×#432311yescharacteristic
416C4C2×#6699111yescharacteristic
417C2—21no—
418C2—21no—
419C2—162no—
420C2—882no—
421C2#1307068212yesdirect product factor
422C2C2×#1062268511yescharacteristic
subgroupG/H
centerC22#10622685
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#495C2
socleC22×C11#459
prime radicalC2×#10622760C2
hypercenterC2×#495D11
hypocenterC11C2×#2212
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
3. C2×#10622313C2semidirect
4. #13070682C2direct (N × H)
5. C2×#10622101C2semidirect
6. C2×#10622203C2semidirect
7. C2×#10622201C2semidirect
8. C2×C11×#495C2semidirect
16. C11×#495C22semidirect
20. #10622792C22semidirect
31. #10622313C22semidirect
32. #10622203C22semidirect
33. #10622201C22semidirect
34. #10622101C22semidirect
150. C2×#495D11semidirect
214. #495C2×D11semidirect
295. C2×C11#2212semidirect
358. C11C2×#2212semidirect
421. C2#13070682direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227922
C2×#106227602
C2×#106223132
#130706822
C2×#106221012
C2×#106222032
C2×#106222012
C2×C11×#4952
C2×#221211