Finite Group Databasebeta

← C2×#13070685 #14908145

Subgroups — C2×#13070685 #14908145

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×#10622808C211yesmaximal, characteristic, complemented
2C2×#10622806C211yesmaximal, characteristic
3C2×#10622309C211yesmaximal, characteristic, complemented
4#13070685C218yesmaximal, direct product factor
5C2×#10622101C211yesmaximal, characteristic, complemented
6C2×#10622134C211yesmaximal, characteristic, complemented
7C2×#10622133C211yesmaximal, characteristic, complemented
8C2×C11×#443C211yesmaximal, characteristic, complemented
9C2×C11×#135C2211yescharacteristic
10C2×C11×#131—21no—
11C22×Dic44C2211yescharacteristic
12C22×D88C2211yescharacteristic
13C22×#4314—21no—
14C2×#66928—21no—
15C11×#443—22no—
16C11×#443C2214yescomplemented
17C2×C11×#108C2211yescharacteristic
18C2×C11×#104—21no—
19C2×C4×C8×C11C2211yescharacteristic
20#10622808—22no—
21#10622808C2214yescomplemented
22#10622806—22no—
23#10622806C2214yes—
24C2×#66893—21no—
25C2×#66892—21no—
26C2×#66891—21no—
27C2×#66890—21no—
28C2×#66876C2211yescharacteristic
29C2×#66876C2211yescharacteristic
30#10622309—22no—
31#10622309C2214yescomplemented
32#10622134C2214yescomplemented
33#10622133C2214yescomplemented
34#10622101C2214yescomplemented
35C2×C11×#41—21no—
36C22×D44—21no—
37C22×Dic22—21no—
38C11×#135—21no—
39C11×#135—21no—
40C11×#135D412yes—
41C11×#135C2312yes—
42C2×C11×Q16D411yescharacteristic
43C2×C11×SD16—21no—
44C2×C11×D8D411yescharacteristic
45C11×#131—24no—
46C11×#131—42no—
47C2×C11×M16—21no—
48C2×C11×M16—41no—
49C22×C8×C11—41no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×(C2×D11)⋊C4—42no—
54C2×Dic44—21no—
55C2×Dic44—21no—
56C2×Dic44—21no—
57C2×Dic44—21no—
58C2×Dic44—21no—
59C2×Dic44C2312yes—
60C2×D88—21no—
61C2×D88—21no—
62C2×D88—21no—
63C2×D88—21no—
64C2×D88—21no—
65C2×D88C2312yes—
66C2×#4314—24no—
67C2×#4314—41no—
68C2×#4314—41no—
69C2×#4314—42no—
70#66928—24no—
71#66928—42no—
72C11×#108—21no—
73C11×#108C2312yes—
74C11×#104—24no—
75C4×C8×C11D412yes—
76C4×C8×C11C2312yes—
77#66893—24no—
78#66892—24no—
79#66891—24no—
80#66890—24no—
81#66876—21no—
82#66876—21no—
83#66876C2312yes—
84#66876C2312yes—
85C2×C11⋊C16—21no—
86C2×C11⋊C16—21no—
87C2×#2212—111nomaximal, Sylow
88C23×D11—41no—
89C11×#41—22no—
90C11×#41—22no—
91C11×#41—41no—
92C11×#41—41no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—21no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×Dic11—41no—
100C2×D44—22no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C11×Q16—21no—
113C11×Q16C2×D412yes—
114C11×SD16—22no—
115C11×SD16—22no—
116C11×D8—21no—
117C11×D8C2×D412yes—
118C11×M16—22no—
119C11×M16—44no—
120C11×M16—41no—
121C2×C8×C11—44no—
122C2×C8×C11—41no—
123C2×C8×C11D811yescharacteristic
124C2×C8×C11D811yescharacteristic
125C2×C8×C11D812yes—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D412yes—
130C2×C8×C11#4111yescharacteristic
131C2×C8×C11#4111yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C42×C11—21no—
134C42×C11C2×D412yes—
135(C2×D11)⋊C4—48no—
136Dic44—22no—
137Dic44—22no—
138Dic44—41no—
139Dic44—41no—
140D88—22no—
141D88—22no—
142D88—41no—
143D88—41no—
144#4314—44no—
145#4314—44no—
146C11⋊C16—22no—
147C11⋊C16—22no—
148C2×#510—111no—
149C2×#509—111no—
150C2×#495—111no—
151C2×#443D1111yescharacteristic, complemented
152#2212—118no—
153C2×#364—111no—
154C2×#362—111no—
155C2×#361—111no—
156C23×C11—41no—
157C23×C11AGL(1,ℤ/8)11yescharacteristic
158C22×D11—42no—
159C22×D11—84no—
160C22×D11—81no—
161C22×D11—81no—
162Q8×C11—22no—
163Q8×C11—41no—
164D4×C11—22no—
165D4×C11—42no—
166D4×C11—42no—
167D4×C11—41no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×Dic11—42no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182D44—42no—
183D44—42no—
184D44—81no—
185D44—81no—
186Dic22—42no—
187Dic22—42no—
188Dic22—81no—
189Dic22—81no—
190C8×C11—42no—
191C8×C11#12111yescharacteristic
192C8×C11#12111yescharacteristic
193C8×C11C2×D812yes—
194C8×C11C2×D812yes—
195C8×C11C22×D411yescharacteristic
196C8×C11C2×#4111yescharacteristic
197C2×#135C2×D1111yescharacteristic
198C22×Q16—111no—
199C22×SD16—221no—
200C22×D8—111no—
201C2×#131—21no—
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×M32—111no—
212C2×M32—111no—
213#495—114no—
214#495—222no—
215#443—22no—
216#443C2×D1114yescomplemented
217C2×#108C2×D1111yescharacteristic
218C2×#104—21no—
219C2×C4×C8C2×D1111yescharacteristic
220#364—114no—
221#362—114no—
222#361—114no—
223C22×C11—22no—
224C22×C11—42no—
225C22×C11—82no—
226C22×C11#45911yescharacteristic
227C22×C11#45911yescharacteristic
228C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C2×D11—84no—
230C2×D11—82no—
231C2×D11—162no—
232C2×D11—162no—
233C4×C11—42no—
234C4×C11—42no—
235C4×C11#45911yescharacteristic
236C4×C11#45911yescharacteristic
237C4×C11C2×#12111yescharacteristic
238C4×C11C22×D811yescharacteristic
239Dic11—82no—
240C2×#41—21no—
241C22×Q8—221no—
242C22×D4—221no—
243#135—21no—
244#135—21no—
245#135D4412yes—
246#135C22×D1112yes—
247C2×Q16—112no—
248C2×Q16—221no—
249C2×Q16—221no—
250C2×Q16—221no—
251C2×Q16—221no—
252C2×Q16—221no—
253C2×Q16D4411yescharacteristic
254C2×SD16—21no—
255C2×SD16—224no—
256C2×SD16—441no—
257C2×SD16—441no—
258C2×SD16—442no—
259C2×D8—112no—
260C2×D8—221no—
261C2×D8—221no—
262C2×D8—221no—
263C2×D8—221no—
264C2×D8—221no—
265C2×D8D4411yescharacteristic
266#131—24no—
267#131—42no—
268C2×M16—21no—
269C2×M16—41no—
270C22×C8—41no—
271C22×C8C22⋊D1111yescharacteristic
272C22×C8C22×D1111yescharacteristic
273#124—224no—
274#124—442no—
275C2×C22⋊C4—442no—
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—21no—
288#108C22×D1112yes—
289#104—24no—
290C4×C8C22⋊D1112yes—
291C4×C8C22×D1112yes—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—82no—
295C2×C11#221212yescomplemented
296C2×C11C2×#45911yescharacteristic
297D11—162no—
298C24—441no—
299#41—22no—
300#41—22no—
301#41—41no—
302#41—41no—
303C2×Q8—21no—
304C2×Q8—222no—
305C2×Q8—441no—
306C2×Q8—441no—
307C2×Q8—441no—
308C2×Q8—441no—
309C2×Q8—441no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—222no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—441no—
321C22×C4C2×C22⋊D1111yescharacteristic
322Q16—21no—
323Q16—222no—
324Q16—222no—
325Q16—441no—
326Q16—441no—
327Q16C2×D4412yes—
328SD16—22no—
329SD16—22no—
330SD16—444no—
331SD16—444no—
332D8—21no—
333D8—222no—
334D8—222no—
335D8—441no—
336D8—441no—
337D8C2×D4412yes—
338M16—22no—
339M16—41no—
340M16—44no—
341C2×C8—41no—
342C2×C8—44no—
343C2×C8#432311yescharacteristic
344C2×C8#432311yescharacteristic
345C2×C8#432312yes—
346C2×C8C2×D4411yescharacteristic
347C2×C8C2×D4411yescharacteristic
348C2×C8#433911yescharacteristic
349C2×C8#433911yescharacteristic
350C2×C8C2×C22⋊D1111yescharacteristic
351C2×C8C2×C22⋊D1112yes—
352C2×C8C23×D1111yescharacteristic
353C22⋊C4—448no—
354C42—21no—
355C42C2×C22⋊D1112yes—
356C16—222no—
357C16—222no—
358C11C2×#221211yescharacteristic, complemented, Sylow
359C23—41no—
360C23—442no—
361C23—884no—
362C23—881no—
363C23—881no—
364C23#6700211yescharacteristic
365Q8—22no—
366Q8—41no—
367Q8—442no—
368Q8—442no—
369Q8—881no—
370Q8—881no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—41no—
375D4—442no—
376D4—442no—
377D4—881no—
378D4—881no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—442no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4#6698311yescharacteristic
388C2×C4#6698311yescharacteristic
389C2×C4C2×#432311yescharacteristic
390C2×C4C2×#432311yescharacteristic
391C2×C4#6700211yescharacteristic
392C2×C4C22×C22⋊D1111yescharacteristic
393C8—42no—
394C8#6698311yescharacteristic
395C8#6698311yescharacteristic
396C8C2×#432312yes—
397C8C2×#432312yes—
398C8C22×D4411yescharacteristic
399C8C2×#433911yescharacteristic
400C22—22no—
401C22—42no—
402C22—82no—
403C22—884no—
404C22—882no—
405C22—1762no—
406C22—1762no—
407C22#1062262811yescharacteristic
408C22#1062262811yescharacteristic
409C22C2×#6700211yescharacteristic
410C4—42no—
411C4—42no—
412C4—882no—
413C4#1062262811yescharacteristic
414C4#1062262811yescharacteristic
415C4C2×#6698311yescharacteristic
416C4C22×#432311yescharacteristic
417C2—21no—
418C2—21no—
419C2—82no—
420C2—1762no—
421C2#1307068512yesdirect product factor
422C2C2×#1062262811yescharacteristic
subgroupG/H
centerC22#10622628
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#443C2
socleC22×C11#459
prime radicalC2×#10622806C2
hypercenterC2×#443D11
hypocenterC11C2×#2212
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
1. C2×#10622808C2semidirect
3. C2×#10622309C2semidirect
4. #13070685C2direct (N × H)
5. C2×#10622101C2semidirect
6. C2×#10622134C2semidirect
7. C2×#10622133C2semidirect
8. C2×C11×#443C2semidirect
16. C11×#443C22semidirect
21. #10622808C22semidirect
31. #10622309C22semidirect
32. #10622134C22semidirect
33. #10622133C22semidirect
34. #10622101C22semidirect
151. C2×#443D11semidirect
216. #443C2×D11semidirect
295. C2×C11#2212semidirect
358. C11C2×#2212semidirect
421. C2#13070685direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106228062
C2×#106223092
#130706852
C2×#106221012
C2×#106221342
C2×#106221332
C2×C11×#4432
C2×#221211