Finite Group Databasebeta

← C2×#13070686 #14908146

Subgroups — C2×#13070686 #14908146

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×#10622522C211yesmaximal, characteristic, complemented
2C2×#10622521C211yesmaximal, characteristic
3C2×#10622309C211yesmaximal, characteristic, complemented
4C2×#10622313C211yesmaximal, characteristic, complemented
5#13070686C218yesmaximal, direct product factor
6C2×#10622155C211yesmaximal, characteristic, complemented
7C2×#10622154C211yesmaximal, characteristic, complemented
8C2×C11×#364C211yesmaximal, characteristic, complemented
9C22×Dic44C2211yescharacteristic
10C2×#66957C2211yescharacteristic
11C22×D88C2211yescharacteristic
12C22×#4314—21no—
13C2×#66954—21no—
14C2×#66928—21no—
15C2×C11×M32C2211yescharacteristic
16C2×C11×M32C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C2×#66883C2211yescharacteristic
19C2×#66869—21no—
20#10622522—22no—
21#10622522C2214yescomplemented
22#10622521—22no—
23#10622521C2214yes—
24C2×Dic88—21no—
25C2×#66864—21no—
26C2×#66864—21no—
27C2×D176—21no—
28#10622313—22no—
29#10622313C2214yescomplemented
30#10622309—22no—
31#10622309C2214yescomplemented
32C11×#364C2214yescomplemented
33#10622155C2214yescomplemented
34#10622154C2214yescomplemented
35C2×#4339—21no—
36C22×D44—21no—
37C22×Dic22—21no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×(C2×D11)⋊C4—42no—
42C2×#4318—21no—
43C2×Dic44—21no—
44C2×Dic44—21no—
45C2×Dic44—21no—
46C2×Dic44—21no—
47C2×Dic44—21no—
48C2×Dic44D411yescharacteristic
49C2×Dic44C2312yes—
50#66957—21no—
51#66957—21no—
52#66957D412yes—
53#66957C2312yes—
54C2×D88—21no—
55C2×D88—21no—
56C2×D88—21no—
57C2×D88—21no—
58C2×D88—21no—
59C2×D88D411yescharacteristic
60C2×D88C2312yes—
61C2×#4314—21no—
62C2×#4314—24no—
63C2×#4314—41no—
64C2×#4314—41no—
65C2×#4314—42no—
66#66954—24no—
67#66954—42no—
68C2×#4313—41no—
69C2×C8×D11—41no—
70#66928—24no—
71#66928—42no—
72C11×M32—21no—
73C11×M32—21no—
74C11×M32C2312yes—
75C11×M32C2312yes—
76C2×C11×C16—21no—
77C2×C11×C16—21no—
78C4×C8×C11D412yes—
79C4×C8×C11C2312yes—
80#66883—21no—
81#66883C2312yes—
82#66869—24no—
83Dic88—24no—
84#66864—24no—
85#66864—24no—
86D176—24no—
87C2×#2212—111nomaximal, Sylow
88C23×D11—41no—
89C22×C4×C11—21no—
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92C22×Dic11—41no—
93#4339—22no—
94#4339—22no—
95#4339—41no—
96#4339—41no—
97C2×D44—21no—
98C2×D44—22no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C2×C8×C11D811yescharacteristic
113C2×C8×C11D811yescharacteristic
114C2×C8×C11D812yes—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D412yes—
119C2×C8×C11#4111yescharacteristic
120C2×C8×C11#4111yescharacteristic
121C2×C8×C11C2411yescharacteristic
122C42×C11—21no—
123C42×C11C2×D412yes—
124(C2×D11)⋊C4—48no—
125#4318—22no—
126#4318—41no—
127C2×C11⋊C8—41no—
128Dic44—21no—
129Dic44—22no—
130Dic44—22no—
131Dic44—41no—
132Dic44—41no—
133Dic44C2×D412yes—
134D88—21no—
135D88—22no—
136D88—22no—
137D88—41no—
138D88—41no—
139D88C2×D412yes—
140#4314—22no—
141#4314—22no—
142#4314—44no—
143#4314—44no—
144#4313—44no—
145C8×D11—44no—
146C11×C16—22no—
147C11×C16—22no—
148C2×#510—111no—
149C2×#509—111no—
150C2×#495—111no—
151C2×#443—111no—
152#2212—118no—
153C2×#364D1111yescharacteristic, complemented
154C2×#362—111no—
155C2×#361—111no—
156C23×C11AGL(1,ℤ/8)11yescharacteristic
157C22×D11—41no—
158C22×D11—42no—
159C22×D11—84no—
160C22×D11—81no—
161C22×D11—81no—
162C2×C4×C11—22no—
163C2×C4×C11—42no—
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C22⋊D11—42no—
171C22⋊D11—42no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176D44—22no—
177D44—42no—
178D44—42no—
179D44—41no—
180D44—81no—
181D44—81no—
182C4×D11—42no—
183C4×D11—42no—
184Dic22—22no—
185Dic22—41no—
186Dic22—42no—
187Dic22—42no—
188Dic22—81no—
189Dic22—81no—
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×Q16—111no—
199C22×SD16—221no—
200C22×D8—111no—
201C2×#131—221no—
202C2×#124—221no—
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×M32C2×D1111yescharacteristic
212C2×M32C2×D1111yescharacteristic
213#495—114no—
214#495—222no—
215#443—114no—
216#443—222no—
217C2×#108—111no—
218C2×#104—221no—
219C2×C4×C8C2×D1111yescharacteristic
220#364C2×D1114yescomplemented
221#362—114no—
222#361—114no—
223C22×C11—22no—
224C22×C11#45911yescharacteristic
225C22×C11#45911yescharacteristic
226C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C2×D11—42no—
228C2×D11—82no—
229C2×D11—84no—
230C2×D11—82no—
231C2×D11—162no—
232C2×D11—162no—
233C4×C11—42no—
234C4×C11#45911yescharacteristic
235C4×C11#45911yescharacteristic
236C4×C11C2×#12111yescharacteristic
237C4×C11C22×D811yescharacteristic
238Dic11—42no—
239Dic11—82no—
240C2×#41—221no—
241C22×Q8—221no—
242C22×D4—221no—
243#135—112no—
244#135—112no—
245#135—221no—
246#135—221no—
247C2×Q16—111no—
248C2×Q16—112no—
249C2×Q16—221no—
250C2×Q16—221no—
251C2×Q16—221no—
252C2×Q16—221no—
253C2×Q16—221no—
254C2×SD16—224no—
255C2×SD16—221no—
256C2×SD16—441no—
257C2×SD16—441no—
258C2×SD16—442no—
259C2×D8—111no—
260C2×D8—112no—
261C2×D8—221no—
262C2×D8—221no—
263C2×D8—221no—
264C2×D8—221no—
265C2×D8—221no—
266#131—224no—
267#131—442no—
268C2×M16—221no—
269C2×M16—441no—
270C22×C8—441no—
271C22×C8D4411yescharacteristic
272C22×C8C22×D1111yescharacteristic
273#124—224no—
274#124—442no—
275C2×C22⋊C4—442no—
276C2×C42D4411yescharacteristic
277Q32—224no—
278SD32—224no—
279SD32—224no—
280D16—224no—
281M32—21no—
282M32—21no—
283M32C22×D1112yes—
284M32C22×D1112yes—
285C2×C16—21no—
286C2×C16—21no—
287#108—112no—
288#108—221no—
289#104—224no—
290C4×C8D4412yes—
291C4×C8C22×D1112yes—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11#221212yescomplemented
295C2×C11C2×#45911yescharacteristic
296D11—82no—
297D11—162no—
298C24—441no—
299#41—222no—
300#41—222no—
301#41—441no—
302#41—441no—
303C2×Q8—221no—
304C2×Q8—222no—
305C2×Q8—441no—
306C2×Q8—441no—
307C2×Q8—441no—
308C2×Q8—441no—
309C2×Q8—441no—
310C2×D4—221no—
311C2×D4—222no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C22×C4—21no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4C2×D4411yescharacteristic
322Q16—112no—
323Q16—221no—
324Q16—222no—
325Q16—222no—
326Q16—441no—
327Q16—441no—
328SD16—222no—
329SD16—222no—
330SD16—444no—
331SD16—444no—
332D8—112no—
333D8—221no—
334D8—222no—
335D8—222no—
336D8—441no—
337D8—441no—
338M16—222no—
339M16—441no—
340M16—444no—
341C2×C8—441no—
342C2×C8—444no—
343C2×C8D8811yescharacteristic
344C2×C8D8811yescharacteristic
345C2×C8D8812yes—
346C2×C8C2×D4411yescharacteristic
347C2×C8C2×D4412yes—
348C2×C8D4×D1111yescharacteristic
349C2×C8D4×D1111yescharacteristic
350C2×C8#434311yescharacteristic
351C2×C8#434311yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C22⋊C4—448no—
354C42—21no—
355C42C2×D4412yes—
356C16—22no—
357C16—22no—
358C11C2×#221211yescharacteristic, complemented, Sylow
359C23—441no—
360C23—442no—
361C23—884no—
362C23—881no—
363C23—881no—
364C23#6696111yescharacteristic
365Q8—222no—
366Q8—441no—
367Q8—442no—
368Q8—442no—
369Q8—881no—
370Q8—881no—
371D4—222no—
372D4—442no—
373D4—442no—
374D4—442no—
375D4—442no—
376D4—441no—
377D4—881no—
378D4—881no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—441no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4#6694811yescharacteristic
388C2×C4#6694811yescharacteristic
389C2×C4C2×D8811yescharacteristic
390C2×C4C2×D8811yescharacteristic
391C2×C4#6696111yescharacteristic
392C2×C4C22×D4411yescharacteristic
393C8—442no—
394C8#6694811yescharacteristic
395C8#6694811yescharacteristic
396C8C2×D8812yes—
397C8C2×D8812yes—
398C8C2×D4×D1111yescharacteristic
399C8C2×#434311yescharacteristic
400C22—22no—
401C22—442no—
402C22—884no—
403C22—882no—
404C22—882no—
405C22—1762no—
406C22—1762no—
407C22#1062245611yescharacteristic
408C22#1062245611yescharacteristic
409C22C2×#6696111yescharacteristic
410C4—42no—
411C4—442no—
412C4—882no—
413C4#1062245611yescharacteristic
414C4#1062245611yescharacteristic
415C4C2×#6694811yescharacteristic
416C4C22×D8811yescharacteristic
417C2—21no—
418C2—21no—
419C2—882no—
420C2—1762no—
421C2#1307068612yesdirect product factor
422C2C2×#1062245611yescharacteristic
subgroupG/H
centerC22#10622456
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#364C2
socleC22×C11#459
prime radicalC2×#10622521C2
hypercenterC2×#364D11
hypocenterC11C2×#2212
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

Complements

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

NH ≅ G/Ntype
1. C2×#10622522C2semidirect
3. C2×#10622309C2semidirect
4. C2×#10622313C2semidirect
5. #13070686C2direct (N × H)
6. C2×#10622155C2semidirect
7. C2×#10622154C2semidirect
8. C2×C11×#364C2semidirect
21. #10622522C22semidirect
29. #10622313C22semidirect
31. #10622309C22semidirect
32. C11×#364C22semidirect
33. #10622155C22semidirect
34. #10622154C22semidirect
153. C2×#364D11semidirect
220. #364C2×D11semidirect
294. C2×C11#2212semidirect
358. C11C2×#2212semidirect
421. C2#13070686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225222
C2×#106225212
C2×#106223092
C2×#106223132
#130706862
C2×#106221552
C2×#106221542
C2×C11×#3642
C2×#221211